Math 111 - Sept 26, 2011

Test 2.3-3.5 - Oct 5 (perhaps - not likely - 7).

Solve

Learn Math Equation: y(^ 4)^ + 2 y(^ 2)^ - 9 9 = 0 let Learn Math Equation: x = y(^ 2)^

Learn Math Equation: x(^ 2)^ + 2 x - 9 9 = 0

Learn Math Equation:(( x + 1 1))(( x - 9)) = 0

Learn Math Equation: x = - 1 1 or Learn Math Equation: x = 9

Learn Math Equation: y(^ 2)^ = - 1 1 or Learn Math Equation: y(^ 2)^ = 9

Learn Math Equation: y = i(r,r 1 1)r or Learn Math Equation: y = - i(r,r 1 1)r or Learn Math Equation: y = 3 or Learn Math Equation: y = - 3

Learn Math Equation: y =s+ i(r,r 1 1)r ,s+ 3

3.2 Quadratics that we can't factor:

Quadratic formula: Learn Math Equation: a x(^ 2)^ + b x + c = 0 then Learn Math Equation: x =(/ - bs+(r,r b(^ 2)^ - 4 a c)r,/ 2 a)/

I will also show you completing the square...

Ex: Learn Math Equation: x(^ 2)^ + 2 x + 5 = 0 Can't be factored...

Learn Math Equation: x =(/ - 2s+(r,r 2(^ 2)^ - 4(( 1))(( 5)))r,/ 2(( 1)))/ =(/ - 2s+(r,r 4 - 2 0)r,/ 2)/ =(/ - 2s+(r,r - 1 6)r,/ 2)/ =(/ - 2s+ 4 i,/ 2)/ = - 1s+ 2 i

Learn Math Equation: x = - 1 + 2 i or Learn Math Equation: x = - 1 - 2 i are the answers...

Check my work...

Learn Math Equation:(( - 1 + 2 i))(^ 2)^ + 2(( - 1 + 2 i)) + 5 note Learn Math Equation:(( - 1 + 2 i))(^ 2)^ =(( - 1 + 2 i))(( - 1 + 2 i))

Learn Math Equation: 1 - 2 i - 2 i - 4 - 2 + 4 i + 5 = 0 yes...

Same problem by completing the square...

Learn Math Equation: x(^ 2)^ + 2 x + 5 = 0 move the 5 to other side

Learn Math Equation: x(^ 2)^ + 2 x = - 5 add 1 to both sides Learn Math Equation:(((/ b,/ 2)/))(^ 2)^

Learn Math Equation: x(^ 2)^ + 2 x + 1 = - 4 factor the left side

Learn Math Equation:(( x + 1))(^ 2)^ = - 4 take square roots

Learn Math Equation: x + 1 =s+ 2 i subtract 1 from both sides

Learn Math Equation: x = - 1s+ 2 i

Another

Learn Math Equation: x(^ 2)^ - 5 x + 8 = 0

Learn Math Equation: x(^ 2)^ - 5 x = - 8

Learn Math Equation: x(^ 2)^ - 5 x +(/ 2 5,/ 4)/ = -(/ 3 2,/ 4)/ +(/ 2 5,/ 4)/

Learn Math Equation:(( x -(/ 5,/ 2)/))(^ 2)^ = -(/ 7,/ 4)/

Learn Math Equation: x -(/ 5,/ 2)/ =s+(/ i(r,r 7)r,/ 2)/

Learn Math Equation: x =(/ 5,/ 2)/s+(/(r,r 7)r,/ 2)/ i =(/ 5s+ i(r,r 7)r,/ 2)/

also by quad form...

Learn Math Equation: x =(/ 5s+(r,r 2 5 - 4s* 8)r,/ 2)/

Learn Math Equation: x =(/ 5s+(r,r 2 5 - 3 2)r,/ 2)/

Learn Math Equation: x =(/ 5s+ i(r,r 7)r,/ 2)/

Another:

Learn Math Equation: 3 x(^ 2)^ - 7 x - 1 5 = 0

Learn Math Equation: x =(/ 7s+(r,r 4 9 - 4(( 3))(( - 1 5)))r,/ 2(( 3)))/

Learn Math Equation: x =(/ 7s+(r,r 4 9 + 1 8 0)r,/ 6)/

Learn Math Equation: x =(/ 7s+(r,r 2 2 9)r,/ 6)/

By completing the square:

Learn Math Equation: 3 x(^ 2)^ - 7 x = 1 5

Learn Math Equation: x(^ 2)^ -(/ 7,/ 3)/ x = 5

Learn Math Equation: x(^ 2)^ -(/ 7,/ 3)/ x +(/ 4 9,/ 3 6)/ =(/ 4 9,/ 3 6)/ +(/ 1 8 0,/ 3 6)/

Learn Math Equation:(( x -(/ 7,/ 6)/))(^ 2)^ =(/ 2 2 9,/ 3 6)/

Learn Math Equation: x -(/ 7,/ 6)/ =(/s+(r,r 2 2 9)r,/ 6)/

Learn Math Equation: x =(/ 7s+(r,r 2 2 9)r,/ 6)/

Learn Math Graph:400 400 -14.254799008369446 1.0 22.301998019218445 -10.227698981761932 1.0 10.380298912525177 g true Function -0.805 3.395 false \3\x(^\2)^\-\7\x\-\1\5 Freehand 60 -1.435 -0.14 -1.4699999 -0.105 -1.4699999 -0.07 -1.4699999 -0.035 -1.4699999 0.0 -1.435 0.035 -1.435 0.07 -1.435 0.07 -1.4 0.105 -1.4 0.105 -1.4 0.14 -1.365 0.14 -1.365 0.14 -1.3299999 0.14 -1.3299999 0.105 -1.3299999 0.105 -1.3299999 0.07 -1.3299999 0.035 -1.3299999 0.0 -1.3299999 -0.035 -1.365 -0.035 -1.365 -0.035 -1.4 -0.035 -1.4 -0.07 -1.435 -0.07 -1.435 -0.035 -1.435 -0.035 -1.435 0.0 -1.435 0.0 -1.435 0.07 -1.4 0.07 -1.4 0.105 -1.365 0.14 -1.365 0.14 -1.3299999 0.175 -1.3299999 0.175 -1.3299999 0.175 -1.2950001 0.175 -1.2950001 0.175 -1.2950001 0.14 -1.2950001 0.14 -1.2950001 0.14 -1.2950001 0.07 -1.3299999 0.07 -1.3299999 0.0 -1.365 0.0 -1.365 0.0 -1.365 0.0 -1.365 0.0 -1.4 0.035 -1.4 0.105 -1.4 0.175 -1.365 0.175 -1.365 0.175 -1.365 0.175 -1.365 0.175 -1.365 0.14 -1.3299999 0.14 -1.3299999 0.105 -1.3299999 0.105 Color red Freehand 66 3.7800002 0.035 3.7450001 0.035 3.7099998 0.0 3.7099998 0.0 3.7099998 0.0 3.6749997 0.0 3.6749997 0.0 3.6749997 0.0 3.6399999 0.035 3.6399999 0.035 3.6399999 0.07 3.6399999 0.105 3.6749997 0.14 3.6749997 0.14 3.6749997 0.175 3.7099998 0.175 3.7099998 0.175 3.7099998 0.175 3.7450001 0.175 3.7450001 0.14 3.7450001 0.14 3.7450001 0.105 3.7450001 0.105 3.7450001 0.07 3.7450001 0.035 3.7450001 0.0 3.7099998 -0.035 3.6749997 -0.035 3.6749997 -0.035 3.6749997 -0.035 3.6399999 -0.035 3.6399999 -0.035 3.6399999 -0.035 3.6399999 0.0 3.6399999 0.07 3.6399999 0.14 3.6749997 0.14 3.6749997 0.175 3.6749997 0.175 3.7099998 0.175 3.7099998 0.175 3.7099998 0.175 3.7450001 0.14 3.7450001 0.14 3.7450001 0.14 3.7450001 0.105 3.7450001 0.105 3.7450001 0.035 3.7099998 0.0 3.7099998 0.0 3.6749997 0.0 3.6399999 0.0 3.6399999 0.0 3.6399999 0.0 3.605 0.035 3.605 0.035 3.605 0.07 3.605 0.07 3.6399999 0.105 3.6399999 0.105 3.6749997 0.14 3.6749997 0.14 3.6749997 0.14 3.7099998 0.14 3.7099998 0.105 3.7099998 0.105 Color red

Learn Math Equation: x =(/ - bs+(r,r b(^ 2)^ - 4 a c)r,/ 2 a)/

Learn Math Equation: b(^ 2)^ - 4 a c is called the discrimate:

if the disc. is positive then the (two) answers will be real

if the disc. is negitive then the answers will be complex (they will have i's in them)

if the disc. is zero then there is only one answer ( Learn Math Equation: -(/ b,/ 2 a)/)

Learn Math Graph:400 400 -7.0 1.0 7.0 -7.0 1.0 7.0 g true Function 3.1499999 3.8500001 false \x(^\2)^\-\2\x\+\1 Color red Freehand 19 2.87 1.8199999 2.9399998 1.8199999 2.9399998 1.8199999 2.9399998 1.8199999 2.9399998 1.8199999 2.9399998 1.8199999 2.9399998 1.785 2.9399998 1.75 2.9399998 1.715 2.9399998 1.68 2.9399998 1.5749999 2.9399998 1.505 2.9399998 1.4 2.9399998 1.365 2.9399998 1.26 2.9399998 1.225 2.9399998 1.19 2.9399998 1.19 2.9399998 1.19 Color red Freehand 11 3.045 1.4699999 3.08 1.4699999 3.115 1.4699999 3.115 1.4699999 3.1850002 1.225 3.08 1.1550001 3.01 1.1550001 2.9750001 1.12 2.9750001 1.12 2.9399998 1.12 2.9399998 1.12 Color red Freehand 25 3.395 2.1000001 3.43 2.135 3.4650002 2.17 3.4650002 2.205 3.4650002 2.205 3.5 2.17 3.5349998 2.17 3.5349998 2.135 3.57 2.1000001 3.57 2.0649998 3.57 2.03 3.5349998 1.995 3.4650002 1.8900001 3.395 1.8549999 3.36 1.8549999 3.36 1.8549999 3.36 1.8549999 3.36 1.8549999 3.395 1.8900001 3.4650002 1.9250001 3.4650002 1.9250001 3.5 1.9250001 3.5349998 1.9250001 3.5349998 1.8900001 3.5349998 1.8900001 Color red Freehand 11 3.5349998 1.435 3.57 1.4 3.605 1.4 3.605 1.4 3.6399999 1.4 3.6399999 1.4 3.6749997 1.4 3.6749997 1.4 3.7099998 1.4 3.7099998 1.4 3.7099998 1.4 Color red Freehand 14 3.99 1.75 4.025 1.68 3.99 1.68 3.99 1.68 3.99 1.645 3.99 1.61 3.99 1.5749999 3.99 1.54 3.99 1.4699999 3.99 1.4699999 4.025 1.435 4.06 1.435 4.06 1.435 4.06 1.435 Color red Freehand 12 4.165 1.715 4.165 1.68 4.165 1.645 4.1299996 1.61 4.1299996 1.54 4.1299996 1.505 4.1299996 1.4699999 4.1299996 1.4 4.1299996 1.2950001 4.1299996 1.26 4.1299996 1.19 4.1299996 1.19 Color red Freehand 34 4.585 1.435 4.5499997 1.435 4.515 1.4699999 4.48 1.4699999 4.41 1.4699999 4.41 1.4699999 4.375 1.4699999 4.375 1.435 4.34 1.435 4.34 1.4 4.3050003 1.365 4.3050003 1.3299999 4.3050003 1.26 4.3050003 1.26 4.3050003 1.225 4.34 1.225 4.41 1.225 4.41 1.26 4.48 1.2950001 4.48 1.2950001 4.515 1.3299999 4.515 1.3299999 4.515 1.365 4.5499997 1.365 4.5499997 1.3299999 4.5499997 1.3299999 4.5499997 1.2950001 4.515 1.2950001 4.515 1.26 4.515 1.225 4.515 1.19 4.515 1.19 4.515 1.1550001 4.515 1.1550001 Color red Freehand 19 4.83 1.365 4.865 1.365 4.865 1.4 4.865 1.4 4.83 1.4 4.83 1.4 4.795 1.4 4.795 1.4 4.76 1.4 4.725 1.365 4.725 1.3299999 4.69 1.2950001 4.69 1.2950001 4.69 1.225 4.69 1.19 4.725 1.1550001 4.725 1.1550001 4.76 1.1550001 4.76 1.1550001 Color red Freehand 12 5.11 1.505 5.145 1.4699999 5.1800003 1.435 5.215 1.435 5.25 1.435 5.25 1.435 5.285 1.435 5.3199997 1.435 5.355 1.435 5.355 1.435 5.355 1.4699999 5.355 1.4699999 Color red Freehand 8 5.145 1.2950001 5.145 1.26 5.145 1.225 5.145 1.225 5.1800003 1.225 5.215 1.225 5.25 1.225 5.25 1.225 Color red Freehand 29 6.0550003 1.54 5.985 1.505 5.915 1.54 5.915 1.54 5.845 1.505 5.81 1.4699999 5.775 1.4699999 5.74 1.435 5.74 1.4 5.705 1.365 5.705 1.3299999 5.67 1.26 5.67 1.19 5.67 1.1550001 5.705 1.12 5.74 1.12 5.74 1.12 5.81 1.12 5.845 1.12 5.8799996 1.1550001 6.0550003 1.26 6.125 1.365 6.125 1.435 6.16 1.505 6.16 1.5749999 6.16 1.61 6.125 1.645 6.09 1.68 6.09 1.68 Color red Freehand 163 1.085 0.0 1.085 -0.035 1.085 -0.035 1.0500001 -0.035 1.0500001 -0.07 1.0500001 -0.07 1.015 -0.07 1.015 -0.07 0.98 -0.105 0.98 -0.105 0.94500005 -0.105 0.90999997 -0.105 0.90999997 -0.105 0.90999997 -0.105 0.90999997 -0.105 0.90999997 -0.105 0.90999997 -0.07 0.90999997 -0.07 0.94500005 -0.07 0.94500005 -0.035 0.94500005 -0.035 0.98 -0.035 0.98 -0.035 0.98 -0.035 0.98 -0.07 0.98 -0.105 0.98 -0.105 0.98 -0.105 0.94500005 -0.105 0.94500005 -0.105 0.94500005 -0.105 0.90999997 -0.105 0.90999997 -0.105 0.90999997 0.07 0.94500005 0.07 0.94500005 0.035 0.98 0.0 0.98 0.0 0.98 0.0 0.98 -0.035 0.98 -0.035 0.94500005 -0.035 0.94500005 -0.07 0.94500005 -0.07 0.90999997 -0.07 0.875 -0.07 0.875 -0.035 0.875 0.0 0.875 0.0 0.875 0.035 0.875 0.035 0.875 0.07 0.875 0.07 0.90999997 0.07 0.90999997 0.07 0.94500005 0.07 0.94500005 0.07 0.94500005 0.07 0.98 0.07 0.98 0.035 0.98 0.0 0.98 -0.07 0.94500005 -0.07 0.94500005 -0.07 0.94500005 -0.07 0.90999997 -0.07 0.90999997 -0.07 0.90999997 -0.07 0.90999997 -0.035 0.875 -0.035 0.90999997 0.0 0.90999997 0.0 0.90999997 0.0 0.94500005 0.0 0.94500005 0.0 0.98 0.035 1.015 0.035 1.015 0.0 1.015 -0.035 1.015 -0.035 1.015 -0.035 1.015 -0.07 1.015 -0.07 1.015 -0.07 0.98 -0.07 0.98 -0.07 0.98 -0.07 0.94500005 -0.07 0.94500005 0.0 0.94500005 0.0 0.94500005 0.035 0.94500005 0.035 0.94500005 0.07 0.98 0.07 0.98 0.07 0.98 0.07 1.015 0.07 1.015 0.07 1.0500001 0.07 1.085 0.035 1.085 0.0 1.085 0.0 1.085 0.0 1.085 -0.035 1.085 -0.035 1.0500001 -0.07 1.0500001 -0.07 1.0500001 -0.07 1.015 -0.07 1.015 -0.105 0.94500005 -0.07 0.94500005 -0.035 0.94500005 0.0 0.94500005 0.035 0.94500005 0.035 0.94500005 0.07 0.98 0.07 0.98 0.105 1.015 0.105 1.0500001 0.105 1.0500001 0.105 1.085 0.07 1.085 0.07 1.085 0.07 1.085 0.035 1.085 0.0 1.085 -0.035 1.085 -0.07 1.0500001 -0.105 1.0500001 -0.105 1.015 -0.105 1.015 -0.14 1.015 -0.14 0.98 -0.105 0.98 -0.105 0.94500005 -0.105 0.94500005 -0.07 0.94500005 -0.07 0.94500005 -0.035 0.94500005 0.035 0.94500005 0.07 0.94500005 0.07 0.94500005 0.105 0.98 0.105 0.98 0.105 1.015 0.14 1.015 0.14 1.0500001 0.14 1.0500001 0.14 1.085 0.105 1.085 0.035 1.085 0.035 1.085 0.0 1.0500001 0.0 1.0500001 -0.035 0.98 -0.035 0.98 -0.035 0.94500005 -0.035 0.90999997 0.0 0.94500005 0.0 0.94500005 0.0 1.015 0.0 1.015 0.0 Color red Function -0.52500004 5.705 false \x(^\2)^\-\2\x\+\3 Color blue Freehand 19 -6.335 5.705 -6.23 5.845 -6.23 5.8799996 -6.23 5.915 -6.23 5.915 -6.23 5.915 -6.23 5.915 -6.23 5.81 -6.23 5.6 -6.23 5.53 -6.23 5.46 -6.23 5.285 -6.23 5.25 -6.23 5.11 -6.23 5.04 -6.1949997 4.97 -6.1949997 4.935 -6.1949997 4.9 -6.1949997 4.9 Color blue Freehand 22 -6.23 5.0750003 -6.1949997 5.11 -6.1949997 5.145 -6.1949997 5.145 -6.1949997 5.1800003 -6.1949997 5.215 -6.125 5.285 -6.0550003 5.3199997 -6.02 5.3199997 -6.02 5.3199997 -6.02 5.285 -5.985 5.25 -5.985 5.0750003 -6.02 4.935 -6.0550003 4.9 -6.0550003 4.83 -6.09 4.795 -6.125 4.76 -6.16 4.725 -6.1949997 4.725 -6.23 4.725 -6.23 4.725 Color blue Freehand 19 -5.845 6.02 -5.81 6.09 -5.775 6.16 -5.775 6.16 -5.74 6.16 -5.705 6.125 -5.705 6.125 -5.635 6.0550003 -5.635 5.985 -5.67 5.985 -5.74 5.8799996 -5.775 5.845 -5.775 5.845 -5.775 5.845 -5.775 5.8799996 -5.74 5.8799996 -5.635 5.8799996 -5.565 5.845 -5.565 5.845 Color blue Freehand 6 -5.635 5.215 -5.565 5.1800003 -5.46 5.215 -5.39 5.25 -5.355 5.25 -5.355 5.25 Color blue Freehand 12 -4.97 5.775 -4.97 5.705 -5.0049996 5.705 -5.0049996 5.565 -5.04 5.4950004 -5.04 5.4249997 -5.04 5.39 -5.0049996 5.285 -5.0049996 5.25 -4.935 5.1800003 -4.9 5.1800003 -4.9 5.1800003 Color blue Freehand 12 -4.655 5.705 -4.655 5.635 -4.655 5.6 -4.69 5.565 -4.69 5.4950004 -4.69 5.39 -4.725 5.3199997 -4.725 5.1800003 -4.76 5.0750003 -4.76 5.0049996 -4.76 4.935 -4.76 4.935 Color blue Freehand 5 -4.3050003 5.3199997 -4.34 5.355 -4.41 5.0750003 -4.375 5.0750003 -4.375 5.0750003 Color blue Freehand 8 -4.27 5.1800003 -4.27 5.145 -4.27 5.11 -4.27 5.0750003 -4.27 5.04 -4.27 5.0049996 -4.235 4.97 -4.235 4.97 Color blue Freehand 13 -3.6749997 5.285 -3.7099998 5.285 -3.7800002 5.285 -3.815 5.25 -3.8500001 5.215 -3.8500001 5.1800003 -3.885 5.145 -3.885 5.0750003 -3.885 5.04 -3.8500001 4.97 -3.7450001 4.935 -3.57 5.0049996 -3.57 5.0049996 Color blue Freehand 26 -4.97 5.74 -4.97 5.775 -4.97 5.775 -4.97 5.775 -4.97 5.775 -4.97 5.775 -4.97 5.775 -4.97 5.74 -5.0049996 5.6 -5.0049996 5.4950004 -5.0049996 5.4249997 -5.0049996 5.355 -4.97 5.3199997 -4.935 5.285 -4.935 5.25 -4.83 5.25 -4.76 5.285 -4.725 5.285 -4.6200004 5.3199997 -4.6200004 5.355 -4.5499997 5.355 -4.5499997 5.39 -4.5499997 5.39 -4.5499997 5.39 -4.5499997 5.39 -4.5499997 5.39 Color blue Freehand 12 -4.725 5.74 -4.725 5.705 -4.725 5.635 -4.76 5.39 -4.76 5.25 -4.76 5.145 -4.76 5.0049996 -4.76 4.865 -4.76 4.76 -4.76 4.655 -4.76 4.655 -4.76 4.655 Color blue Freehand 8 -3.4650002 5.215 -3.43 5.215 -3.36 5.25 -3.255 5.285 -3.22 5.285 -3.1850002 5.285 -3.115 5.285 -3.115 5.285 Color blue Freehand 8 -3.325 5.0049996 -3.325 4.935 -3.29 4.935 -3.255 4.935 -3.22 4.935 -3.1499999 4.97 -3.045 5.0049996 -3.045 5.0049996 Color blue Freehand 20 -2.695 5.11 -2.73 5.145 -2.73 5.1800003 -2.73 5.215 -2.765 5.25 -2.765 5.25 -2.765 5.25 -2.765 5.25 -2.695 5.25 -2.6599998 5.25 -2.625 5.25 -2.5900002 5.25 -2.52 5.25 -2.415 5.25 -2.415 5.25 -2.38 5.25 -2.38 5.25 -2.38 5.25 -2.38 5.25 -2.38 5.25 Color blue Freehand 36 -1.9250001 5.635 -1.9250001 5.705 -1.9250001 5.705 -1.96 5.705 -1.995 5.705 -2.03 5.705 -2.0649998 5.635 -2.17 5.53 -2.205 5.4249997 -2.205 5.39 -2.17 5.355 -2.135 5.355 -2.0649998 5.3199997 -1.995 5.3199997 -1.96 5.3199997 -1.9250001 5.3199997 -1.8900001 5.285 -1.8549999 5.285 -1.8549999 5.25 -1.8549999 5.215 -1.8549999 5.0750003 -1.8900001 4.97 -1.9250001 4.9 -1.96 4.9 -1.995 4.865 -2.03 4.865 -2.0649998 4.9 -2.0649998 4.935 -2.0649998 5.0049996 -2.03 5.145 -2.03 5.215 -1.995 5.25 -1.9250001 5.39 -1.8199999 5.53 -1.785 5.6 -1.785 5.6 Color blue Function 3.1850002 -1.3299999 false \x(^\2)^\-\2\x\-\4 Color green Freehand 10 -6.3700004 -2.1000001 -6.335 -2.135 -6.335 -2.17 -6.335 -2.205 -6.3700004 -2.24 -6.3700004 -2.38 -6.3700004 -2.45 -6.335 -2.625 -6.335 -2.73 -6.335 -2.73 Color green Freehand 15 -6.2999997 -2.485 -6.265 -2.485 -6.265 -2.45 -6.23 -2.45 -6.125 -2.415 -6.09 -2.45 -6.02 -2.485 -6.02 -2.52 -6.02 -2.52 -6.02 -2.625 -6.125 -2.835 -6.1949997 -2.905 -6.1949997 -2.905 -6.23 -2.905 -6.23 -2.905 Color green Freehand 18 -5.8799996 -1.61 -5.845 -1.5749999 -5.775 -1.505 -5.74 -1.4699999 -5.705 -1.4699999 -5.67 -1.4699999 -5.635 -1.505 -5.635 -1.5749999 -5.705 -1.715 -5.775 -1.8549999 -5.81 -1.8549999 -5.81 -1.8549999 -5.81 -1.8549999 -5.775 -1.8199999 -5.67 -1.785 -5.635 -1.785 -5.53 -1.8549999 -5.53 -1.8549999 Color green Freehand 7 -5.565 -2.415 -5.53 -2.45 -5.4950004 -2.45 -5.4249997 -2.415 -5.355 -2.415 -5.285 -2.415 -5.285 -2.415 Color green Freehand 11 -5.145 -1.8900001 -5.11 -1.96 -5.11 -1.995 -5.11 -2.03 -5.11 -2.1000001 -5.11 -2.205 -5.11 -2.3100002 -5.0750003 -2.345 -5.0049996 -2.415 -4.97 -2.415 -4.97 -2.415 Color green Freehand 7 -4.83 -1.9250001 -4.795 -1.995 -4.795 -2.0649998 -4.83 -2.1000001 -4.83 -2.2749999 -4.865 -2.87 -4.865 -2.87 Color green Freehand 18 -4.41 -2.345 -4.48 -2.2749999 -4.515 -2.2749999 -4.6200004 -2.2749999 -4.69 -2.3100002 -4.69 -2.345 -4.76 -2.415 -4.76 -2.555 -4.76 -2.5900002 -4.725 -2.5900002 -4.655 -2.5900002 -4.6200004 -2.5900002 -4.6200004 -2.5900002 -4.585 -2.555 -4.515 -2.52 -4.515 -2.52 -4.48 -2.765 -4.48 -2.765 Color green Freehand 14 -3.8500001 -2.205 -3.885 -2.24 -3.92 -2.2749999 -3.99 -2.345 -4.095 -2.485 -4.095 -2.52 -4.095 -2.5900002 -4.095 -2.625 -4.025 -2.695 -3.99 -2.695 -3.885 -2.695 -3.8500001 -2.695 -3.815 -2.6599998 -3.815 -2.6599998 Color green Freehand 6 -3.325 -2.38 -3.29 -2.45 -3.255 -2.45 -3.115 -2.45 -3.08 -2.45 -3.08 -2.45 Color green Freehand 8 -3.36 -2.5900002 -3.325 -2.695 -3.255 -2.73 -3.1850002 -2.73 -3.1499999 -2.73 -3.115 -2.73 -3.01 -2.695 -3.01 -2.695 Color green Freehand 18 -2.87 -2.2749999 -2.8 -2.17 -2.6599998 -2.1000001 -2.625 -2.0649998 -2.555 -2.0649998 -2.555 -2.0649998 -2.485 -2.17 -2.485 -2.52 -2.52 -2.5900002 -2.5900002 -2.73 -2.6599998 -2.765 -2.625 -2.625 -2.625 -2.555 -2.555 -2.52 -2.415 -2.555 -2.3100002 -2.5900002 -2.24 -2.625 -2.24 -2.625 Color green Freehand 19 -1.8549999 -2.17 -1.8900001 -2.17 -1.9250001 -2.24 -1.96 -2.2749999 -2.03 -2.345 -2.0649998 -2.415 -2.135 -2.5900002 -2.135 -2.695 -2.0649998 -2.835 -1.96 -2.835 -1.8900001 -2.765 -1.715 -2.5900002 -1.68 -2.485 -1.68 -2.415 -1.715 -2.24 -1.75 -2.17 -1.785 -2.17 -1.8549999 -2.17 -1.8549999 -2.17 Color green Freehand 36 -1.435 -0.035 -1.4 0.0 -1.365 0.0 -1.3299999 0.035 -1.2950001 0.035 -1.2950001 0.035 -1.26 0.0 -1.26 0.035 -1.26 0.035 -1.2950001 0.07 -1.2950001 0.105 -1.26 0.14 -1.26 0.14 -1.26 0.035 -1.2950001 -0.07 -1.3299999 -0.105 -1.3299999 -0.14 -1.3299999 -0.105 -1.3299999 -0.035 -1.2950001 0.0 -1.225 0.07 -1.19 0.07 -1.2950001 -0.105 -1.365 -0.07 -1.365 0.0 -1.365 0.035 -1.225 0.14 -1.19 0.14 -1.19 0.105 -1.19 0.035 -1.26 0.0 -1.26 0.0 -1.2950001 0.0 -1.26 0.105 -1.085 0.175 -1.085 0.175 Color green Freehand 25 3.22 0.14 3.29 0.14 3.29 0.14 3.29 0.105 3.08 0.035 3.115 0.14 3.1850002 0.21 3.255 0.245 3.325 0.175 3.29 0.07 3.255 0.035 3.1850002 0.035 3.115 0.035 3.08 0.105 3.115 0.14 3.1850002 0.175 3.29 0.175 3.325 0.14 3.325 0.07 3.325 0.0 3.29 0.0 3.255 0.175 3.29 0.175 3.325 0.175 3.325 0.175 Color green

Learn Math Equation: 5 x(^ 4)^ - 2 x(^ 2)^ + 8 = 0 let Learn Math Equation: z = x(^ 2)^

Learn Math Equation: 5 z(^ 2)^ - 2 z + 8 = 0

Learn Math Equation: z =(/ 2s+(r,r 4 - 1 6 0)r,/ 2(( 5)))/ =(/ 2s+ i(r,r 1 5 6)r,/ 1 0)/ =(/ 2s+ 2 i(r,r 3 9)r,/ 1 0)/ =(/ 1s+ i(r,r 3 9)r,/ 5)/

Learn Math Equation: x =s+(r,r(/ 1s+ i(r,r 3 9)r,/ 5)/)r =s.