2x^2+24x=256

Solution for 2x^2+24x=256 equation:

Simplifying
2x2 + 24x = 256

Reorder the terms:
24x + 2x2 = 256

Solving
24x + 2x2 = 256

Solving for variable 'x'.

Reorder the terms:
-256 + 24x + 2x2 = 256 + -256

Combine like terms: 256 + -256 = 0
-256 + 24x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-128 + 12x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-128 + 12x + x2)' equal to zero and attempt to solve:

Simplifying
-128 + 12x + x2 = 0

Solving
-128 + 12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '128' to each side of the equation.
-128 + 12x + 128 + x2 = 0 + 128

Reorder the terms:
-128 + 128 + 12x + x2 = 0 + 128

Combine like terms: -128 + 128 = 0
0 + 12x + x2 = 0 + 128
12x + x2 = 0 + 128

Combine like terms: 0 + 128 = 128
12x + x2 = 128

The x term is 12x.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12x + 36 + x2 = 128 + 36

Reorder the terms:
36 + 12x + x2 = 128 + 36

Combine like terms: 128 + 36 = 164
36 + 12x + x2 = 164

Factor a perfect square on the left side:
(x + 6)(x + 6) = 164

Calculate the square root of the right side: 12.806248475

Break this problem into two subproblems by setting 
(x + 6) equal to 12.806248475 and -12.806248475.

Subproblem 1
x + 6 = 12.806248475

Simplifying
x + 6 = 12.806248475

Reorder the terms:
6 + x = 12.806248475

Solving
6 + x = 12.806248475

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x = 12.806248475 + -6

Combine like terms: 6 + -6 = 0
0 + x = 12.806248475 + -6
x = 12.806248475 + -6

Combine like terms: 12.806248475 + -6 = 6.806248475
x = 6.806248475

Simplifying
x = 6.806248475

Subproblem 2
x + 6 = -12.806248475

Simplifying
x + 6 = -12.806248475

Reorder the terms:
6 + x = -12.806248475

Solving
6 + x = -12.806248475

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x = -12.806248475 + -6

Combine like terms: 6 + -6 = 0
0 + x = -12.806248475 + -6
x = -12.806248475 + -6

Combine like terms: -12.806248475 + -6 = -18.806248475
x = -18.806248475

Simplifying
x = -18.806248475

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.806248475, -18.806248475}
Solution
x = {6.806248475, -18.806248475}