x^2-24x-126=0

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Solution for x^2-24x-126=0 equation: 


Simplifying
x2 + -24x + -126 = 0

Reorder the terms:
-126 + -24x + x2 = 0

Solving
-126 + -24x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '126' to each side of the equation.
-126 + -24x + 126 + x2 = 0 + 126

Reorder the terms:
-126 + 126 + -24x + x2 = 0 + 126

Combine like terms: -126 + 126 = 0
0 + -24x + x2 = 0 + 126
-24x + x2 = 0 + 126

Combine like terms: 0 + 126 = 126
-24x + x2 = 126

The x term is -24x.  Take half its coefficient (-12).
Square it (144) and add it to both sides.

Add '144' to each side of the equation.
-24x + 144 + x2 = 126 + 144

Reorder the terms:
144 + -24x + x2 = 126 + 144

Combine like terms: 126 + 144 = 270
144 + -24x + x2 = 270

Factor a perfect square on the left side:
(x + -12)(x + -12) = 270

Calculate the square root of the right side: 16.431676725

Break this problem into two subproblems by setting 
(x + -12) equal to 16.431676725 and -16.431676725.


Subproblem 1
x + -12 = 16.431676725

Simplifying
x + -12 = 16.431676725

Reorder the terms:
-12 + x = 16.431676725

Solving
-12 + x = 16.431676725

Solving for variable 'x'.

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

Add '12' to each side of the equation.
-12 + 12 + x = 16.431676725 + 12

Combine like terms: -12 + 12 = 0
0 + x = 16.431676725 + 12
x = 16.431676725 + 12

Combine like terms: 16.431676725 + 12 = 28.431676725
x = 28.431676725

Simplifying
x = 28.431676725


Subproblem 2
x + -12 = -16.431676725

Simplifying
x + -12 = -16.431676725

Reorder the terms:
-12 + x = -16.431676725

Solving
-12 + x = -16.431676725

Solving for variable 'x'.

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

Add '12' to each side of the equation.
-12 + 12 + x = -16.431676725 + 12

Combine like terms: -12 + 12 = 0
0 + x = -16.431676725 + 12
x = -16.431676725 + 12

Combine like terms: -16.431676725 + 12 = -4.431676725
x = -4.431676725

Simplifying
x = -4.431676725


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {28.431676725, -4.431676725}

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