x^2+4x-132=0

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Solution for x^2+4x-132=0 equation:


Simplifying
x2 + 4x + -132 = 0

Reorder the terms:
-132 + 4x + x2 = 0

Solving
-132 + 4x + 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 + 4x + 132 + x2 = 0 + 132

Reorder the terms:
-132 + 132 + 4x + x2 = 0 + 132

Combine like terms: -132 + 132 = 0
0 + 4x + x2 = 0 + 132
4x + x2 = 0 + 132

Combine like terms: 0 + 132 = 132
4x + x2 = 132

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 132 + 4

Reorder the terms:
4 + 4x + x2 = 132 + 4

Combine like terms: 132 + 4 = 136
4 + 4x + x2 = 136

Factor a perfect square on the left side:
(x + 2)(x + 2) = 136

Calculate the square root of the right side: 11.66190379

Break this problem into two subproblems by setting 
(x + 2) equal to 11.66190379 and -11.66190379.

Subproblem 1

x + 2 = 11.66190379 Simplifying x + 2 = 11.66190379 Reorder the terms: 2 + x = 11.66190379 Solving 2 + x = 11.66190379 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 11.66190379 + -2 Combine like terms: 2 + -2 = 0 0 + x = 11.66190379 + -2 x = 11.66190379 + -2 Combine like terms: 11.66190379 + -2 = 9.66190379 x = 9.66190379 Simplifying x = 9.66190379

Subproblem 2

x + 2 = -11.66190379 Simplifying x + 2 = -11.66190379 Reorder the terms: 2 + x = -11.66190379 Solving 2 + x = -11.66190379 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -11.66190379 + -2 Combine like terms: 2 + -2 = 0 0 + x = -11.66190379 + -2 x = -11.66190379 + -2 Combine like terms: -11.66190379 + -2 = -13.66190379 x = -13.66190379 Simplifying x = -13.66190379

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.66190379, -13.66190379}

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