4x^2+64x-520=0

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Solution for 4x^2+64x-520=0 equation: 


Simplifying
4x2 + 64x + -520 = 0

Reorder the terms:
-520 + 64x + 4x2 = 0

Solving
-520 + 64x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-130 + 16x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-130 + 16x + x2)' equal to zero and attempt to solve:

Simplifying
-130 + 16x + x2 = 0

Solving
-130 + 16x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '130' to each side of the equation.
-130 + 16x + 130 + x2 = 0 + 130

Reorder the terms:
-130 + 130 + 16x + x2 = 0 + 130

Combine like terms: -130 + 130 = 0
0 + 16x + x2 = 0 + 130
16x + x2 = 0 + 130

Combine like terms: 0 + 130 = 130
16x + x2 = 130

The x term is 16x.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16x + 64 + x2 = 130 + 64

Reorder the terms:
64 + 16x + x2 = 130 + 64

Combine like terms: 130 + 64 = 194
64 + 16x + x2 = 194

Factor a perfect square on the left side:
(x + 8)(x + 8) = 194

Calculate the square root of the right side: 13.928388277

Break this problem into two subproblems by setting 
(x + 8) equal to 13.928388277 and -13.928388277.


Subproblem 1
x + 8 = 13.928388277

Simplifying
x + 8 = 13.928388277

Reorder the terms:
8 + x = 13.928388277

Solving
8 + x = 13.928388277

Solving for variable 'x'.

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

Add '-8' to each side of the equation.
8 + -8 + x = 13.928388277 + -8

Combine like terms: 8 + -8 = 0
0 + x = 13.928388277 + -8
x = 13.928388277 + -8

Combine like terms: 13.928388277 + -8 = 5.928388277
x = 5.928388277

Simplifying
x = 5.928388277


Subproblem 2
x + 8 = -13.928388277

Simplifying
x + 8 = -13.928388277

Reorder the terms:
8 + x = -13.928388277

Solving
8 + x = -13.928388277

Solving for variable 'x'.

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

Add '-8' to each side of the equation.
8 + -8 + x = -13.928388277 + -8

Combine like terms: 8 + -8 = 0
0 + x = -13.928388277 + -8
x = -13.928388277 + -8

Combine like terms: -13.928388277 + -8 = -21.928388277
x = -21.928388277

Simplifying
x = -21.928388277


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.928388277, -21.928388277}
Solution
x = {5.928388277, -21.928388277}

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