x^2+8x-132=0

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Solution for x^2+8x-132=0 equation:


Simplifying
x2 + 8x + -132 = 0

Reorder the terms:
-132 + 8x + x2 = 0

Solving
-132 + 8x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '132' to each side of the equation.
-132 + 8x + 132 + x2 = 0 + 132

Reorder the terms:
-132 + 132 + 8x + x2 = 0 + 132

Combine like terms: -132 + 132 = 0
0 + 8x + x2 = 0 + 132
8x + x2 = 0 + 132

Combine like terms: 0 + 132 = 132
8x + x2 = 132

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = 132 + 16

Reorder the terms:
16 + 8x + x2 = 132 + 16

Combine like terms: 132 + 16 = 148
16 + 8x + x2 = 148

Factor a perfect square on the left side:
(x + 4)(x + 4) = 148

Calculate the square root of the right side: 12.165525061

Break this problem into two subproblems by setting 
(x + 4) equal to 12.165525061 and -12.165525061.

Subproblem 1

x + 4 = 12.165525061 Simplifying x + 4 = 12.165525061 Reorder the terms: 4 + x = 12.165525061 Solving 4 + x = 12.165525061 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 12.165525061 + -4 Combine like terms: 4 + -4 = 0 0 + x = 12.165525061 + -4 x = 12.165525061 + -4 Combine like terms: 12.165525061 + -4 = 8.165525061 x = 8.165525061 Simplifying x = 8.165525061

Subproblem 2

x + 4 = -12.165525061 Simplifying x + 4 = -12.165525061 Reorder the terms: 4 + x = -12.165525061 Solving 4 + x = -12.165525061 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -12.165525061 + -4 Combine like terms: 4 + -4 = 0 0 + x = -12.165525061 + -4 x = -12.165525061 + -4 Combine like terms: -12.165525061 + -4 = -16.165525061 x = -16.165525061 Simplifying x = -16.165525061

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.165525061, -16.165525061}

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