x^2+12x-115=0

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Solution for x^2+12x-115=0 equation:


Simplifying
x2 + 12x + -115 = 0

Reorder the terms:
-115 + 12x + x2 = 0

Solving
-115 + 12x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '115' to each side of the equation.
-115 + 12x + 115 + x2 = 0 + 115

Reorder the terms:
-115 + 115 + 12x + x2 = 0 + 115

Combine like terms: -115 + 115 = 0
0 + 12x + x2 = 0 + 115
12x + x2 = 0 + 115

Combine like terms: 0 + 115 = 115
12x + x2 = 115

The x term is 12x.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12x + 36 + x2 = 115 + 36

Reorder the terms:
36 + 12x + x2 = 115 + 36

Combine like terms: 115 + 36 = 151
36 + 12x + x2 = 151

Factor a perfect square on the left side:
(x + 6)(x + 6) = 151

Calculate the square root of the right side: 12.288205727

Break this problem into two subproblems by setting 
(x + 6) equal to 12.288205727 and -12.288205727.

Subproblem 1

x + 6 = 12.288205727 Simplifying x + 6 = 12.288205727 Reorder the terms: 6 + x = 12.288205727 Solving 6 + x = 12.288205727 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 12.288205727 + -6 Combine like terms: 6 + -6 = 0 0 + x = 12.288205727 + -6 x = 12.288205727 + -6 Combine like terms: 12.288205727 + -6 = 6.288205727 x = 6.288205727 Simplifying x = 6.288205727

Subproblem 2

x + 6 = -12.288205727 Simplifying x + 6 = -12.288205727 Reorder the terms: 6 + x = -12.288205727 Solving 6 + x = -12.288205727 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -12.288205727 + -6 Combine like terms: 6 + -6 = 0 0 + x = -12.288205727 + -6 x = -12.288205727 + -6 Combine like terms: -12.288205727 + -6 = -18.288205727 x = -18.288205727 Simplifying x = -18.288205727

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.288205727, -18.288205727}

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