x^2+7x-132=0

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Solution for x^2+7x-132=0 equation:


Simplifying
x2 + 7x + -132 = 0

Reorder the terms:
-132 + 7x + x2 = 0

Solving
-132 + 7x + 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 + 7x + 132 + x2 = 0 + 132

Reorder the terms:
-132 + 132 + 7x + x2 = 0 + 132

Combine like terms: -132 + 132 = 0
0 + 7x + x2 = 0 + 132
7x + x2 = 0 + 132

Combine like terms: 0 + 132 = 132
7x + x2 = 132

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = 132 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 132 + 12.25

Combine like terms: 132 + 12.25 = 144.25
12.25 + 7x + x2 = 144.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 144.25

Calculate the square root of the right side: 12.010412149

Break this problem into two subproblems by setting 
(x + 3.5) equal to 12.010412149 and -12.010412149.

Subproblem 1

x + 3.5 = 12.010412149 Simplifying x + 3.5 = 12.010412149 Reorder the terms: 3.5 + x = 12.010412149 Solving 3.5 + x = 12.010412149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 12.010412149 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 12.010412149 + -3.5 x = 12.010412149 + -3.5 Combine like terms: 12.010412149 + -3.5 = 8.510412149 x = 8.510412149 Simplifying x = 8.510412149

Subproblem 2

x + 3.5 = -12.010412149 Simplifying x + 3.5 = -12.010412149 Reorder the terms: 3.5 + x = -12.010412149 Solving 3.5 + x = -12.010412149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -12.010412149 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -12.010412149 + -3.5 x = -12.010412149 + -3.5 Combine like terms: -12.010412149 + -3.5 = -15.510412149 x = -15.510412149 Simplifying x = -15.510412149

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.510412149, -15.510412149}

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