20x+20-8x*x-24=-16x*x+190x+24

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Solution for 20x+20-8x*x-24=-16x*x+190x+24 equation: 


Simplifying
20x + 20 + -8x * x + -24 = -16x * x + 190x + 24

Multiply x * x
20x + 20 + -8x2 + -24 = -16x * x + 190x + 24

Reorder the terms:
20 + -24 + 20x + -8x2 = -16x * x + 190x + 24

Combine like terms: 20 + -24 = -4
-4 + 20x + -8x2 = -16x * x + 190x + 24

Multiply x * x
-4 + 20x + -8x2 = -16x2 + 190x + 24

Reorder the terms:
-4 + 20x + -8x2 = 24 + 190x + -16x2

Solving
-4 + 20x + -8x2 = 24 + 190x + -16x2

Solving for variable 'x'.

Reorder the terms:
-4 + -24 + 20x + -190x + -8x2 + 16x2 = 24 + 190x + -16x2 + -24 + -190x + 16x2

Combine like terms: -4 + -24 = -28
-28 + 20x + -190x + -8x2 + 16x2 = 24 + 190x + -16x2 + -24 + -190x + 16x2

Combine like terms: 20x + -190x = -170x
-28 + -170x + -8x2 + 16x2 = 24 + 190x + -16x2 + -24 + -190x + 16x2

Combine like terms: -8x2 + 16x2 = 8x2
-28 + -170x + 8x2 = 24 + 190x + -16x2 + -24 + -190x + 16x2

Reorder the terms:
-28 + -170x + 8x2 = 24 + -24 + 190x + -190x + -16x2 + 16x2

Combine like terms: 24 + -24 = 0
-28 + -170x + 8x2 = 0 + 190x + -190x + -16x2 + 16x2
-28 + -170x + 8x2 = 190x + -190x + -16x2 + 16x2

Combine like terms: 190x + -190x = 0
-28 + -170x + 8x2 = 0 + -16x2 + 16x2
-28 + -170x + 8x2 = -16x2 + 16x2

Combine like terms: -16x2 + 16x2 = 0
-28 + -170x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-14 + -85x + 4x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-14 + -85x + 4x2)' equal to zero and attempt to solve:

Simplifying
-14 + -85x + 4x2 = 0

Solving
-14 + -85x + 4x2 = 0

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
-3.5 + -21.25x + x2 = 0

Move the constant term to the right:

Add '3.5' to each side of the equation.
-3.5 + -21.25x + 3.5 + x2 = 0 + 3.5

Reorder the terms:
-3.5 + 3.5 + -21.25x + x2 = 0 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + -21.25x + x2 = 0 + 3.5
-21.25x + x2 = 0 + 3.5

Combine like terms: 0 + 3.5 = 3.5
-21.25x + x2 = 3.5

The x term is -21.25x.  Take half its coefficient (-10.625).
Square it (112.890625) and add it to both sides.

Add '112.890625' to each side of the equation.
-21.25x + 112.890625 + x2 = 3.5 + 112.890625

Reorder the terms:
112.890625 + -21.25x + x2 = 3.5 + 112.890625

Combine like terms: 3.5 + 112.890625 = 116.390625
112.890625 + -21.25x + x2 = 116.390625

Factor a perfect square on the left side:
(x + -10.625)(x + -10.625) = 116.390625

Calculate the square root of the right side: 10.788448684

Break this problem into two subproblems by setting 
(x + -10.625) equal to 10.788448684 and -10.788448684.


Subproblem 1
x + -10.625 = 10.788448684

Simplifying
x + -10.625 = 10.788448684

Reorder the terms:
-10.625 + x = 10.788448684

Solving
-10.625 + x = 10.788448684

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '10.625' to each side of the equation.
-10.625 + 10.625 + x = 10.788448684 + 10.625

Combine like terms: -10.625 + 10.625 = 0.000
0.000 + x = 10.788448684 + 10.625
x = 10.788448684 + 10.625

Combine like terms: 10.788448684 + 10.625 = 21.413448684
x = 21.413448684

Simplifying
x = 21.413448684


Subproblem 2
x + -10.625 = -10.788448684

Simplifying
x + -10.625 = -10.788448684

Reorder the terms:
-10.625 + x = -10.788448684

Solving
-10.625 + x = -10.788448684

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '10.625' to each side of the equation.
-10.625 + 10.625 + x = -10.788448684 + 10.625

Combine like terms: -10.625 + 10.625 = 0.000
0.000 + x = -10.788448684 + 10.625
x = -10.788448684 + 10.625

Combine like terms: -10.788448684 + 10.625 = -0.163448684
x = -0.163448684

Simplifying
x = -0.163448684


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {21.413448684, -0.163448684}
Solution
x = {21.413448684, -0.163448684}

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