2x^2+2x=400

Solution for 2x^2+2x=400 equation:

Simplifying
2x2 + 2x = 400

Reorder the terms:
2x + 2x2 = 400

Solving
2x + 2x2 = 400

Solving for variable 'x'.

Reorder the terms:
-400 + 2x + 2x2 = 400 + -400

Combine like terms: 400 + -400 = 0
-400 + 2x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-200 + x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-200 + x + x2)' equal to zero and attempt to solve:

Simplifying
-200 + x + x2 = 0

Solving
-200 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '200' to each side of the equation.
-200 + x + 200 + x2 = 0 + 200

Reorder the terms:
-200 + 200 + x + x2 = 0 + 200

Combine like terms: -200 + 200 = 0
0 + x + x2 = 0 + 200
x + x2 = 0 + 200

Combine like terms: 0 + 200 = 200
x + x2 = 200

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
x + 0.25 + x2 = 200 + 0.25

Reorder the terms:
0.25 + x + x2 = 200 + 0.25

Combine like terms: 200 + 0.25 = 200.25
0.25 + x + x2 = 200.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 200.25

Calculate the square root of the right side: 14.150971698

Break this problem into two subproblems by setting 
(x + 0.5) equal to 14.150971698 and -14.150971698.

Subproblem 1
x + 0.5 = 14.150971698

Simplifying
x + 0.5 = 14.150971698

Reorder the terms:
0.5 + x = 14.150971698

Solving
0.5 + x = 14.150971698

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 14.150971698 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 14.150971698 + -0.5
x = 14.150971698 + -0.5

Combine like terms: 14.150971698 + -0.5 = 13.650971698
x = 13.650971698

Simplifying
x = 13.650971698

Subproblem 2
x + 0.5 = -14.150971698

Simplifying
x + 0.5 = -14.150971698

Reorder the terms:
0.5 + x = -14.150971698

Solving
0.5 + x = -14.150971698

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -14.150971698 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -14.150971698 + -0.5
x = -14.150971698 + -0.5

Combine like terms: -14.150971698 + -0.5 = -14.650971698
x = -14.650971698

Simplifying
x = -14.650971698

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.650971698, -14.650971698}
Solution
x = {13.650971698, -14.650971698}