x^2+9x-180=0

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Solution for x^2+9x-180=0 equation:


Simplifying
x2 + 9x + -180 = 0

Reorder the terms:
-180 + 9x + x2 = 0

Solving
-180 + 9x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '180' to each side of the equation.
-180 + 9x + 180 + x2 = 0 + 180

Reorder the terms:
-180 + 180 + 9x + x2 = 0 + 180

Combine like terms: -180 + 180 = 0
0 + 9x + x2 = 0 + 180
9x + x2 = 0 + 180

Combine like terms: 0 + 180 = 180
9x + x2 = 180

The x term is 9x.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9x + 20.25 + x2 = 180 + 20.25

Reorder the terms:
20.25 + 9x + x2 = 180 + 20.25

Combine like terms: 180 + 20.25 = 200.25
20.25 + 9x + x2 = 200.25

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 200.25

Calculate the square root of the right side: 14.150971698

Break this problem into two subproblems by setting 
(x + 4.5) equal to 14.150971698 and -14.150971698.

Subproblem 1

x + 4.5 = 14.150971698 Simplifying x + 4.5 = 14.150971698 Reorder the terms: 4.5 + x = 14.150971698 Solving 4.5 + x = 14.150971698 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 14.150971698 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 14.150971698 + -4.5 x = 14.150971698 + -4.5 Combine like terms: 14.150971698 + -4.5 = 9.650971698 x = 9.650971698 Simplifying x = 9.650971698

Subproblem 2

x + 4.5 = -14.150971698 Simplifying x + 4.5 = -14.150971698 Reorder the terms: 4.5 + x = -14.150971698 Solving 4.5 + x = -14.150971698 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -14.150971698 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -14.150971698 + -4.5 x = -14.150971698 + -4.5 Combine like terms: -14.150971698 + -4.5 = -18.650971698 x = -18.650971698 Simplifying x = -18.650971698

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.650971698, -18.650971698}

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