2x^2+12x-876=0

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Solution for 2x^2+12x-876=0 equation: 


Simplifying
2x2 + 12x + -876 = 0

Reorder the terms:
-876 + 12x + 2x2 = 0

Solving
-876 + 12x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-438 + 6x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-438 + 6x + x2)' equal to zero and attempt to solve:

Simplifying
-438 + 6x + x2 = 0

Solving
-438 + 6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '438' to each side of the equation.
-438 + 6x + 438 + x2 = 0 + 438

Reorder the terms:
-438 + 438 + 6x + x2 = 0 + 438

Combine like terms: -438 + 438 = 0
0 + 6x + x2 = 0 + 438
6x + x2 = 0 + 438

Combine like terms: 0 + 438 = 438
6x + x2 = 438

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = 438 + 9

Reorder the terms:
9 + 6x + x2 = 438 + 9

Combine like terms: 438 + 9 = 447
9 + 6x + x2 = 447

Factor a perfect square on the left side:
(x + 3)(x + 3) = 447

Calculate the square root of the right side: 21.142374512

Break this problem into two subproblems by setting 
(x + 3) equal to 21.142374512 and -21.142374512.


Subproblem 1
x + 3 = 21.142374512

Simplifying
x + 3 = 21.142374512

Reorder the terms:
3 + x = 21.142374512

Solving
3 + x = 21.142374512

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = 21.142374512 + -3

Combine like terms: 3 + -3 = 0
0 + x = 21.142374512 + -3
x = 21.142374512 + -3

Combine like terms: 21.142374512 + -3 = 18.142374512
x = 18.142374512

Simplifying
x = 18.142374512


Subproblem 2
x + 3 = -21.142374512

Simplifying
x + 3 = -21.142374512

Reorder the terms:
3 + x = -21.142374512

Solving
3 + x = -21.142374512

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = -21.142374512 + -3

Combine like terms: 3 + -3 = 0
0 + x = -21.142374512 + -3
x = -21.142374512 + -3

Combine like terms: -21.142374512 + -3 = -24.142374512
x = -24.142374512

Simplifying
x = -24.142374512


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {18.142374512, -24.142374512}
Solution
x = {18.142374512, -24.142374512}

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