2x^2+8x=204

Solution for 2x^2+8x=204 equation:

Simplifying
2x2 + 8x = 204

Reorder the terms:
8x + 2x2 = 204

Solving
8x + 2x2 = 204

Solving for variable 'x'.

Reorder the terms:
-204 + 8x + 2x2 = 204 + -204

Combine like terms: 204 + -204 = 0
-204 + 8x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-102 + 4x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-102 + 4x + x2)' equal to zero and attempt to solve:

Simplifying
-102 + 4x + x2 = 0

Solving
-102 + 4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '102' to each side of the equation.
-102 + 4x + 102 + x2 = 0 + 102

Reorder the terms:
-102 + 102 + 4x + x2 = 0 + 102

Combine like terms: -102 + 102 = 0
0 + 4x + x2 = 0 + 102
4x + x2 = 0 + 102

Combine like terms: 0 + 102 = 102
4x + x2 = 102

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 102 + 4

Reorder the terms:
4 + 4x + x2 = 102 + 4

Combine like terms: 102 + 4 = 106
4 + 4x + x2 = 106

Factor a perfect square on the left side:
(x + 2)(x + 2) = 106

Calculate the square root of the right side: 10.295630141

Break this problem into two subproblems by setting 
(x + 2) equal to 10.295630141 and -10.295630141.

Subproblem 1
x + 2 = 10.295630141

Simplifying
x + 2 = 10.295630141

Reorder the terms:
2 + x = 10.295630141

Solving
2 + x = 10.295630141

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 10.295630141 + -2

Combine like terms: 2 + -2 = 0
0 + x = 10.295630141 + -2
x = 10.295630141 + -2

Combine like terms: 10.295630141 + -2 = 8.295630141
x = 8.295630141

Simplifying
x = 8.295630141

Subproblem 2
x + 2 = -10.295630141

Simplifying
x + 2 = -10.295630141

Reorder the terms:
2 + x = -10.295630141

Solving
2 + x = -10.295630141

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -10.295630141 + -2

Combine like terms: 2 + -2 = 0
0 + x = -10.295630141 + -2
x = -10.295630141 + -2

Combine like terms: -10.295630141 + -2 = -12.295630141
x = -12.295630141

Simplifying
x = -12.295630141

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.295630141, -12.295630141}
Solution
x = {8.295630141, -12.295630141}