4x^2-64x-356=0

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Solution for 4x^2-64x-356=0 equation: 


Simplifying
4x2 + -64x + -356 = 0

Reorder the terms:
-356 + -64x + 4x2 = 0

Solving
-356 + -64x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-89 + -16x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-89 + -16x + x2)' equal to zero and attempt to solve:

Simplifying
-89 + -16x + x2 = 0

Solving
-89 + -16x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '89' to each side of the equation.
-89 + -16x + 89 + x2 = 0 + 89

Reorder the terms:
-89 + 89 + -16x + x2 = 0 + 89

Combine like terms: -89 + 89 = 0
0 + -16x + x2 = 0 + 89
-16x + x2 = 0 + 89

Combine like terms: 0 + 89 = 89
-16x + x2 = 89

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 = 89 + 64

Reorder the terms:
64 + -16x + x2 = 89 + 64

Combine like terms: 89 + 64 = 153
64 + -16x + x2 = 153

Factor a perfect square on the left side:
(x + -8)(x + -8) = 153

Calculate the square root of the right side: 12.369316877

Break this problem into two subproblems by setting 
(x + -8) equal to 12.369316877 and -12.369316877.


Subproblem 1
x + -8 = 12.369316877

Simplifying
x + -8 = 12.369316877

Reorder the terms:
-8 + x = 12.369316877

Solving
-8 + x = 12.369316877

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 = 12.369316877 + 8

Combine like terms: -8 + 8 = 0
0 + x = 12.369316877 + 8
x = 12.369316877 + 8

Combine like terms: 12.369316877 + 8 = 20.369316877
x = 20.369316877

Simplifying
x = 20.369316877


Subproblem 2
x + -8 = -12.369316877

Simplifying
x + -8 = -12.369316877

Reorder the terms:
-8 + x = -12.369316877

Solving
-8 + x = -12.369316877

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 = -12.369316877 + 8

Combine like terms: -8 + 8 = 0
0 + x = -12.369316877 + 8
x = -12.369316877 + 8

Combine like terms: -12.369316877 + 8 = -4.369316877
x = -4.369316877

Simplifying
x = -4.369316877


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {20.369316877, -4.369316877}
Solution
x = {20.369316877, -4.369316877}

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