2x^2-12x-360=0

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Solution for 2x^2-12x-360=0 equation: 


Simplifying
2x2 + -12x + -360 = 0

Reorder the terms:
-360 + -12x + 2x2 = 0

Solving
-360 + -12x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-180 + -6x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-180 + -6x + x2)' equal to zero and attempt to solve:

Simplifying
-180 + -6x + x2 = 0

Solving
-180 + -6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '180' to each side of the equation.
-180 + -6x + 180 + x2 = 0 + 180

Reorder the terms:
-180 + 180 + -6x + x2 = 0 + 180

Combine like terms: -180 + 180 = 0
0 + -6x + x2 = 0 + 180
-6x + x2 = 0 + 180

Combine like terms: 0 + 180 = 180
-6x + x2 = 180

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 = 180 + 9

Reorder the terms:
9 + -6x + x2 = 180 + 9

Combine like terms: 180 + 9 = 189
9 + -6x + x2 = 189

Factor a perfect square on the left side:
(x + -3)(x + -3) = 189

Calculate the square root of the right side: 13.747727085

Break this problem into two subproblems by setting 
(x + -3) equal to 13.747727085 and -13.747727085.


Subproblem 1
x + -3 = 13.747727085

Simplifying
x + -3 = 13.747727085

Reorder the terms:
-3 + x = 13.747727085

Solving
-3 + x = 13.747727085

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 = 13.747727085 + 3

Combine like terms: -3 + 3 = 0
0 + x = 13.747727085 + 3
x = 13.747727085 + 3

Combine like terms: 13.747727085 + 3 = 16.747727085
x = 16.747727085

Simplifying
x = 16.747727085


Subproblem 2
x + -3 = -13.747727085

Simplifying
x + -3 = -13.747727085

Reorder the terms:
-3 + x = -13.747727085

Solving
-3 + x = -13.747727085

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 = -13.747727085 + 3

Combine like terms: -3 + 3 = 0
0 + x = -13.747727085 + 3
x = -13.747727085 + 3

Combine like terms: -13.747727085 + 3 = -10.747727085
x = -10.747727085

Simplifying
x = -10.747727085


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.747727085, -10.747727085}
Solution
x = {16.747727085, -10.747727085}

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