x^2+8x=256

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Solution for x^2+8x=256 equation:


Simplifying
x2 + 8x = 256

Reorder the terms:
8x + x2 = 256

Solving
8x + x2 = 256

Solving for variable 'x'.

Reorder the terms:
-256 + 8x + x2 = 256 + -256

Combine like terms: 256 + -256 = 0
-256 + 8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '256' to each side of the equation.
-256 + 8x + 256 + x2 = 0 + 256

Reorder the terms:
-256 + 256 + 8x + x2 = 0 + 256

Combine like terms: -256 + 256 = 0
0 + 8x + x2 = 0 + 256
8x + x2 = 0 + 256

Combine like terms: 0 + 256 = 256
8x + x2 = 256

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = 256 + 16

Reorder the terms:
16 + 8x + x2 = 256 + 16

Combine like terms: 256 + 16 = 272
16 + 8x + x2 = 272

Factor a perfect square on the left side:
(x + 4)(x + 4) = 272

Calculate the square root of the right side: 16.492422502

Break this problem into two subproblems by setting 
(x + 4) equal to 16.492422502 and -16.492422502.

Subproblem 1

x + 4 = 16.492422502 Simplifying x + 4 = 16.492422502 Reorder the terms: 4 + x = 16.492422502 Solving 4 + x = 16.492422502 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 16.492422502 + -4 Combine like terms: 4 + -4 = 0 0 + x = 16.492422502 + -4 x = 16.492422502 + -4 Combine like terms: 16.492422502 + -4 = 12.492422502 x = 12.492422502 Simplifying x = 12.492422502

Subproblem 2

x + 4 = -16.492422502 Simplifying x + 4 = -16.492422502 Reorder the terms: 4 + x = -16.492422502 Solving 4 + x = -16.492422502 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -16.492422502 + -4 Combine like terms: 4 + -4 = 0 0 + x = -16.492422502 + -4 x = -16.492422502 + -4 Combine like terms: -16.492422502 + -4 = -20.492422502 x = -20.492422502 Simplifying x = -20.492422502

Solution

The solution to the problem is based on the solutions from the subproblems. x = {12.492422502, -20.492422502}

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