x^2-12x-117=0

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Solution for x^2-12x-117=0 equation:


Simplifying
x2 + -12x + -117 = 0

Reorder the terms:
-117 + -12x + x2 = 0

Solving
-117 + -12x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '117' to each side of the equation.
-117 + -12x + 117 + x2 = 0 + 117

Reorder the terms:
-117 + 117 + -12x + x2 = 0 + 117

Combine like terms: -117 + 117 = 0
0 + -12x + x2 = 0 + 117
-12x + x2 = 0 + 117

Combine like terms: 0 + 117 = 117
-12x + x2 = 117

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 = 117 + 36

Reorder the terms:
36 + -12x + x2 = 117 + 36

Combine like terms: 117 + 36 = 153
36 + -12x + x2 = 153

Factor a perfect square on the left side:
(x + -6)(x + -6) = 153

Calculate the square root of the right side: 12.369316877

Break this problem into two subproblems by setting 
(x + -6) equal to 12.369316877 and -12.369316877.

Subproblem 1

x + -6 = 12.369316877 Simplifying x + -6 = 12.369316877 Reorder the terms: -6 + x = 12.369316877 Solving -6 + x = 12.369316877 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 = 12.369316877 + 6 Combine like terms: -6 + 6 = 0 0 + x = 12.369316877 + 6 x = 12.369316877 + 6 Combine like terms: 12.369316877 + 6 = 18.369316877 x = 18.369316877 Simplifying x = 18.369316877

Subproblem 2

x + -6 = -12.369316877 Simplifying x + -6 = -12.369316877 Reorder the terms: -6 + x = -12.369316877 Solving -6 + x = -12.369316877 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 = -12.369316877 + 6 Combine like terms: -6 + 6 = 0 0 + x = -12.369316877 + 6 x = -12.369316877 + 6 Combine like terms: -12.369316877 + 6 = -6.369316877 x = -6.369316877 Simplifying x = -6.369316877

Solution

The solution to the problem is based on the solutions from the subproblems. x = {18.369316877, -6.369316877}

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