-4x^2+64x+256=0

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Solution for -4x^2+64x+256=0 equation: 


Simplifying
-4x2 + 64x + 256 = 0

Reorder the terms:
256 + 64x + -4x2 = 0

Solving
256 + 64x + -4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(64 + 16x + -1x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(64 + 16x + -1x2)' equal to zero and attempt to solve:

Simplifying
64 + 16x + -1x2 = 0

Solving
64 + 16x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-64 + -16x + x2 = 0

Move the constant term to the right:

Add '64' to each side of the equation.
-64 + -16x + 64 + x2 = 0 + 64

Reorder the terms:
-64 + 64 + -16x + x2 = 0 + 64

Combine like terms: -64 + 64 = 0
0 + -16x + x2 = 0 + 64
-16x + x2 = 0 + 64

Combine like terms: 0 + 64 = 64
-16x + x2 = 64

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 = 64 + 64

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

Combine like terms: 64 + 64 = 128
64 + -16x + x2 = 128

Factor a perfect square on the left side:
(x + -8)(x + -8) = 128

Calculate the square root of the right side: 11.313708499

Break this problem into two subproblems by setting 
(x + -8) equal to 11.313708499 and -11.313708499.


Subproblem 1
x + -8 = 11.313708499

Simplifying
x + -8 = 11.313708499

Reorder the terms:
-8 + x = 11.313708499

Solving
-8 + x = 11.313708499

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 = 11.313708499 + 8

Combine like terms: -8 + 8 = 0
0 + x = 11.313708499 + 8
x = 11.313708499 + 8

Combine like terms: 11.313708499 + 8 = 19.313708499
x = 19.313708499

Simplifying
x = 19.313708499


Subproblem 2
x + -8 = -11.313708499

Simplifying
x + -8 = -11.313708499

Reorder the terms:
-8 + x = -11.313708499

Solving
-8 + x = -11.313708499

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 = -11.313708499 + 8

Combine like terms: -8 + 8 = 0
0 + x = -11.313708499 + 8
x = -11.313708499 + 8

Combine like terms: -11.313708499 + 8 = -3.313708499
x = -3.313708499

Simplifying
x = -3.313708499


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {19.313708499, -3.313708499}
Solution
x = {19.313708499, -3.313708499}

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