0=x^2+24x-144

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Solution for 0=x^2+24x-144 equation:


Simplifying
0 = x2 + 24x + -144

Reorder the terms:
0 = -144 + 24x + x2

Solving
0 = -144 + 24x + x2

Solving for variable 'x'.

Combine like terms: 0 + 144 = 144
144 + -24x + -1x2 = -144 + 24x + x2 + 144 + -24x + -1x2

Reorder the terms:
144 + -24x + -1x2 = -144 + 144 + 24x + -24x + x2 + -1x2

Combine like terms: -144 + 144 = 0
144 + -24x + -1x2 = 0 + 24x + -24x + x2 + -1x2
144 + -24x + -1x2 = 24x + -24x + x2 + -1x2

Combine like terms: 24x + -24x = 0
144 + -24x + -1x2 = 0 + x2 + -1x2
144 + -24x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
144 + -24x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-144 + 24x + x2 = 0

Move the constant term to the right:

Add '144' to each side of the equation.
-144 + 24x + 144 + x2 = 0 + 144

Reorder the terms:
-144 + 144 + 24x + x2 = 0 + 144

Combine like terms: -144 + 144 = 0
0 + 24x + x2 = 0 + 144
24x + x2 = 0 + 144

Combine like terms: 0 + 144 = 144
24x + x2 = 144

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 = 144 + 144

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

Combine like terms: 144 + 144 = 288
144 + 24x + x2 = 288

Factor a perfect square on the left side:
(x + 12)(x + 12) = 288

Calculate the square root of the right side: 16.970562748

Break this problem into two subproblems by setting 
(x + 12) equal to 16.970562748 and -16.970562748.

Subproblem 1

x + 12 = 16.970562748 Simplifying x + 12 = 16.970562748 Reorder the terms: 12 + x = 16.970562748 Solving 12 + x = 16.970562748 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 = 16.970562748 + -12 Combine like terms: 12 + -12 = 0 0 + x = 16.970562748 + -12 x = 16.970562748 + -12 Combine like terms: 16.970562748 + -12 = 4.970562748 x = 4.970562748 Simplifying x = 4.970562748

Subproblem 2

x + 12 = -16.970562748 Simplifying x + 12 = -16.970562748 Reorder the terms: 12 + x = -16.970562748 Solving 12 + x = -16.970562748 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 = -16.970562748 + -12 Combine like terms: 12 + -12 = 0 0 + x = -16.970562748 + -12 x = -16.970562748 + -12 Combine like terms: -16.970562748 + -12 = -28.970562748 x = -28.970562748 Simplifying x = -28.970562748

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.970562748, -28.970562748}

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