2x^2+4x-396=0

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Solution for 2x^2+4x-396=0 equation: 


Simplifying
2x2 + 4x + -396 = 0

Reorder the terms:
-396 + 4x + 2x2 = 0

Solving
-396 + 4x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-198 + 2x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-198 + 2x + x2)' equal to zero and attempt to solve:

Simplifying
-198 + 2x + x2 = 0

Solving
-198 + 2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '198' to each side of the equation.
-198 + 2x + 198 + x2 = 0 + 198

Reorder the terms:
-198 + 198 + 2x + x2 = 0 + 198

Combine like terms: -198 + 198 = 0
0 + 2x + x2 = 0 + 198
2x + x2 = 0 + 198

Combine like terms: 0 + 198 = 198
2x + x2 = 198

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 198 + 1

Reorder the terms:
1 + 2x + x2 = 198 + 1

Combine like terms: 198 + 1 = 199
1 + 2x + x2 = 199

Factor a perfect square on the left side:
(x + 1)(x + 1) = 199

Calculate the square root of the right side: 14.10673598

Break this problem into two subproblems by setting 
(x + 1) equal to 14.10673598 and -14.10673598.


Subproblem 1
x + 1 = 14.10673598

Simplifying
x + 1 = 14.10673598

Reorder the terms:
1 + x = 14.10673598

Solving
1 + x = 14.10673598

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 14.10673598 + -1

Combine like terms: 1 + -1 = 0
0 + x = 14.10673598 + -1
x = 14.10673598 + -1

Combine like terms: 14.10673598 + -1 = 13.10673598
x = 13.10673598

Simplifying
x = 13.10673598


Subproblem 2
x + 1 = -14.10673598

Simplifying
x + 1 = -14.10673598

Reorder the terms:
1 + x = -14.10673598

Solving
1 + x = -14.10673598

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -14.10673598 + -1

Combine like terms: 1 + -1 = 0
0 + x = -14.10673598 + -1
x = -14.10673598 + -1

Combine like terms: -14.10673598 + -1 = -15.10673598
x = -15.10673598

Simplifying
x = -15.10673598


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.10673598, -15.10673598}
Solution
x = {13.10673598, -15.10673598}

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