(x^2)+24x-11496=0

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Solution for (x^2)+24x-11496=0 equation: 


Simplifying
(x2) + 24x + -11496 = 0
x2 + 24x + -11496 = 0

Reorder the terms:
-11496 + 24x + x2 = 0

Solving
-11496 + 24x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '11496' to each side of the equation.
-11496 + 24x + 11496 + x2 = 0 + 11496

Reorder the terms:
-11496 + 11496 + 24x + x2 = 0 + 11496

Combine like terms: -11496 + 11496 = 0
0 + 24x + x2 = 0 + 11496
24x + x2 = 0 + 11496

Combine like terms: 0 + 11496 = 11496
24x + x2 = 11496

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 = 11496 + 144

Reorder the terms:
144 + 24x + x2 = 11496 + 144

Combine like terms: 11496 + 144 = 11640
144 + 24x + x2 = 11640

Factor a perfect square on the left side:
(x + 12)(x + 12) = 11640

Calculate the square root of the right side: 107.888831674

Break this problem into two subproblems by setting 
(x + 12) equal to 107.888831674 and -107.888831674.


Subproblem 1
x + 12 = 107.888831674

Simplifying
x + 12 = 107.888831674

Reorder the terms:
12 + x = 107.888831674

Solving
12 + x = 107.888831674

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 = 107.888831674 + -12

Combine like terms: 12 + -12 = 0
0 + x = 107.888831674 + -12
x = 107.888831674 + -12

Combine like terms: 107.888831674 + -12 = 95.888831674
x = 95.888831674

Simplifying
x = 95.888831674


Subproblem 2
x + 12 = -107.888831674

Simplifying
x + 12 = -107.888831674

Reorder the terms:
12 + x = -107.888831674

Solving
12 + x = -107.888831674

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 = -107.888831674 + -12

Combine like terms: 12 + -12 = 0
0 + x = -107.888831674 + -12
x = -107.888831674 + -12

Combine like terms: -107.888831674 + -12 = -119.888831674
x = -119.888831674

Simplifying
x = -119.888831674


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {95.888831674, -119.888831674}

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