2x^2+20x-64=0

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Solution for 2x^2+20x-64=0 equation: 


Simplifying
2x2 + 20x + -64 = 0

Reorder the terms:
-64 + 20x + 2x2 = 0

Solving
-64 + 20x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-32 + 10x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-32 + 10x + x2)' equal to zero and attempt to solve:

Simplifying
-32 + 10x + x2 = 0

Solving
-32 + 10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '32' to each side of the equation.
-32 + 10x + 32 + x2 = 0 + 32

Reorder the terms:
-32 + 32 + 10x + x2 = 0 + 32

Combine like terms: -32 + 32 = 0
0 + 10x + x2 = 0 + 32
10x + x2 = 0 + 32

Combine like terms: 0 + 32 = 32
10x + x2 = 32

The x term is 10x.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10x + 25 + x2 = 32 + 25

Reorder the terms:
25 + 10x + x2 = 32 + 25

Combine like terms: 32 + 25 = 57
25 + 10x + x2 = 57

Factor a perfect square on the left side:
(x + 5)(x + 5) = 57

Calculate the square root of the right side: 7.549834435

Break this problem into two subproblems by setting 
(x + 5) equal to 7.549834435 and -7.549834435.


Subproblem 1
x + 5 = 7.549834435

Simplifying
x + 5 = 7.549834435

Reorder the terms:
5 + x = 7.549834435

Solving
5 + x = 7.549834435

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = 7.549834435 + -5

Combine like terms: 5 + -5 = 0
0 + x = 7.549834435 + -5
x = 7.549834435 + -5

Combine like terms: 7.549834435 + -5 = 2.549834435
x = 2.549834435

Simplifying
x = 2.549834435


Subproblem 2
x + 5 = -7.549834435

Simplifying
x + 5 = -7.549834435

Reorder the terms:
5 + x = -7.549834435

Solving
5 + x = -7.549834435

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = -7.549834435 + -5

Combine like terms: 5 + -5 = 0
0 + x = -7.549834435 + -5
x = -7.549834435 + -5

Combine like terms: -7.549834435 + -5 = -12.549834435
x = -12.549834435

Simplifying
x = -12.549834435


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.549834435, -12.549834435}
Solution
x = {2.549834435, -12.549834435}

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