x^2+24x-1196=0

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Solution for x^2+24x-1196=0 equation: 


Simplifying
x2 + 24x + -1196 = 0

Reorder the terms:
-1196 + 24x + x2 = 0

Solving
-1196 + 24x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '1196' to each side of the equation.
-1196 + 24x + 1196 + x2 = 0 + 1196

Reorder the terms:
-1196 + 1196 + 24x + x2 = 0 + 1196

Combine like terms: -1196 + 1196 = 0
0 + 24x + x2 = 0 + 1196
24x + x2 = 0 + 1196

Combine like terms: 0 + 1196 = 1196
24x + x2 = 1196

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 = 1196 + 144

Reorder the terms:
144 + 24x + x2 = 1196 + 144

Combine like terms: 1196 + 144 = 1340
144 + 24x + x2 = 1340

Factor a perfect square on the left side:
(x + 12)(x + 12) = 1340

Calculate the square root of the right side: 36.606010435

Break this problem into two subproblems by setting 
(x + 12) equal to 36.606010435 and -36.606010435.


Subproblem 1
x + 12 = 36.606010435

Simplifying
x + 12 = 36.606010435

Reorder the terms:
12 + x = 36.606010435

Solving
12 + x = 36.606010435

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 = 36.606010435 + -12

Combine like terms: 12 + -12 = 0
0 + x = 36.606010435 + -12
x = 36.606010435 + -12

Combine like terms: 36.606010435 + -12 = 24.606010435
x = 24.606010435

Simplifying
x = 24.606010435


Subproblem 2
x + 12 = -36.606010435

Simplifying
x + 12 = -36.606010435

Reorder the terms:
12 + x = -36.606010435

Solving
12 + x = -36.606010435

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 = -36.606010435 + -12

Combine like terms: 12 + -12 = 0
0 + x = -36.606010435 + -12
x = -36.606010435 + -12

Combine like terms: -36.606010435 + -12 = -48.606010435
x = -48.606010435

Simplifying
x = -48.606010435


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {24.606010435, -48.606010435}

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