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 = 15.10673598
x = 15.10673598

Simplifying
x = 15.10673598


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 = -13.10673598
x = -13.10673598

Simplifying
x = -13.10673598


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

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