x^2-45x-180=0

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Solution for x^2-45x-180=0 equation: 


Simplifying
x2 + -45x + -180 = 0

Reorder the terms:
-180 + -45x + x2 = 0

Solving
-180 + -45x + 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 + -45x + 180 + x2 = 0 + 180

Reorder the terms:
-180 + 180 + -45x + x2 = 0 + 180

Combine like terms: -180 + 180 = 0
0 + -45x + x2 = 0 + 180
-45x + x2 = 0 + 180

Combine like terms: 0 + 180 = 180
-45x + x2 = 180

The x term is -45x.  Take half its coefficient (-22.5).
Square it (506.25) and add it to both sides.

Add '506.25' to each side of the equation.
-45x + 506.25 + x2 = 180 + 506.25

Reorder the terms:
506.25 + -45x + x2 = 180 + 506.25

Combine like terms: 180 + 506.25 = 686.25
506.25 + -45x + x2 = 686.25

Factor a perfect square on the left side:
(x + -22.5)(x + -22.5) = 686.25

Calculate the square root of the right side: 26.196373795

Break this problem into two subproblems by setting 
(x + -22.5) equal to 26.196373795 and -26.196373795.


Subproblem 1
x + -22.5 = 26.196373795

Simplifying
x + -22.5 = 26.196373795

Reorder the terms:
-22.5 + x = 26.196373795

Solving
-22.5 + x = 26.196373795

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '22.5' to each side of the equation.
-22.5 + 22.5 + x = 26.196373795 + 22.5

Combine like terms: -22.5 + 22.5 = 0.0
0.0 + x = 26.196373795 + 22.5
x = 26.196373795 + 22.5

Combine like terms: 26.196373795 + 22.5 = 48.696373795
x = 48.696373795

Simplifying
x = 48.696373795


Subproblem 2
x + -22.5 = -26.196373795

Simplifying
x + -22.5 = -26.196373795

Reorder the terms:
-22.5 + x = -26.196373795

Solving
-22.5 + x = -26.196373795

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '22.5' to each side of the equation.
-22.5 + 22.5 + x = -26.196373795 + 22.5

Combine like terms: -22.5 + 22.5 = 0.0
0.0 + x = -26.196373795 + 22.5
x = -26.196373795 + 22.5

Combine like terms: -26.196373795 + 22.5 = -3.696373795
x = -3.696373795

Simplifying
x = -3.696373795


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {48.696373795, -3.696373795}

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