x^2-12x-240=0

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Solution for x^2-12x-240=0 equation: 


Simplifying
x2 + -12x + -240 = 0

Reorder the terms:
-240 + -12x + x2 = 0

Solving
-240 + -12x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '240' to each side of the equation.
-240 + -12x + 240 + x2 = 0 + 240

Reorder the terms:
-240 + 240 + -12x + x2 = 0 + 240

Combine like terms: -240 + 240 = 0
0 + -12x + x2 = 0 + 240
-12x + x2 = 0 + 240

Combine like terms: 0 + 240 = 240
-12x + x2 = 240

The x term is -12x.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12x + 36 + x2 = 240 + 36

Reorder the terms:
36 + -12x + x2 = 240 + 36

Combine like terms: 240 + 36 = 276
36 + -12x + x2 = 276

Factor a perfect square on the left side:
(x + -6)(x + -6) = 276

Calculate the square root of the right side: 16.613247726

Break this problem into two subproblems by setting 
(x + -6) equal to 16.613247726 and -16.613247726.


Subproblem 1
x + -6 = 16.613247726

Simplifying
x + -6 = 16.613247726

Reorder the terms:
-6 + x = 16.613247726

Solving
-6 + x = 16.613247726

Solving for variable 'x'.

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

Add '6' to each side of the equation.
-6 + 6 + x = 16.613247726 + 6

Combine like terms: -6 + 6 = 0
0 + x = 16.613247726 + 6
x = 16.613247726 + 6

Combine like terms: 16.613247726 + 6 = 22.613247726
x = 22.613247726

Simplifying
x = 22.613247726


Subproblem 2
x + -6 = -16.613247726

Simplifying
x + -6 = -16.613247726

Reorder the terms:
-6 + x = -16.613247726

Solving
-6 + x = -16.613247726

Solving for variable 'x'.

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

Add '6' to each side of the equation.
-6 + 6 + x = -16.613247726 + 6

Combine like terms: -6 + 6 = 0
0 + x = -16.613247726 + 6
x = -16.613247726 + 6

Combine like terms: -16.613247726 + 6 = -10.613247726
x = -10.613247726

Simplifying
x = -10.613247726


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {22.613247726, -10.613247726}

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