x^2+24x-12=180

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Solution for x^2+24x-12=180 equation:


Simplifying
x2 + 24x + -12 = 180

Reorder the terms:
-12 + 24x + x2 = 180

Solving
-12 + 24x + x2 = 180

Solving for variable 'x'.

Reorder the terms:
-12 + -180 + 24x + x2 = 180 + -180

Combine like terms: -12 + -180 = -192
-192 + 24x + x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-192 + 24x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '192' to each side of the equation.
-192 + 24x + 192 + x2 = 0 + 192

Reorder the terms:
-192 + 192 + 24x + x2 = 0 + 192

Combine like terms: -192 + 192 = 0
0 + 24x + x2 = 0 + 192
24x + x2 = 0 + 192

Combine like terms: 0 + 192 = 192
24x + x2 = 192

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 = 192 + 144

Reorder the terms:
144 + 24x + x2 = 192 + 144

Combine like terms: 192 + 144 = 336
144 + 24x + x2 = 336

Factor a perfect square on the left side:
(x + 12)(x + 12) = 336

Calculate the square root of the right side: 18.33030278

Break this problem into two subproblems by setting 
(x + 12) equal to 18.33030278 and -18.33030278.

Subproblem 1

x + 12 = 18.33030278 Simplifying x + 12 = 18.33030278 Reorder the terms: 12 + x = 18.33030278 Solving 12 + x = 18.33030278 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 = 18.33030278 + -12 Combine like terms: 12 + -12 = 0 0 + x = 18.33030278 + -12 x = 18.33030278 + -12 Combine like terms: 18.33030278 + -12 = 6.33030278 x = 6.33030278 Simplifying x = 6.33030278

Subproblem 2

x + 12 = -18.33030278 Simplifying x + 12 = -18.33030278 Reorder the terms: 12 + x = -18.33030278 Solving 12 + x = -18.33030278 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 = -18.33030278 + -12 Combine like terms: 12 + -12 = 0 0 + x = -18.33030278 + -12 x = -18.33030278 + -12 Combine like terms: -18.33030278 + -12 = -30.33030278 x = -30.33030278 Simplifying x = -30.33030278

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.33030278, -30.33030278}

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