x^2-10x-180=0

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Solution for x^2-10x-180=0 equation: 


Simplifying
x2 + -10x + -180 = 0

Reorder the terms:
-180 + -10x + x2 = 0

Solving
-180 + -10x + 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 + -10x + 180 + x2 = 0 + 180

Reorder the terms:
-180 + 180 + -10x + x2 = 0 + 180

Combine like terms: -180 + 180 = 0
0 + -10x + x2 = 0 + 180
-10x + x2 = 0 + 180

Combine like terms: 0 + 180 = 180
-10x + x2 = 180

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = 180 + 25

Reorder the terms:
25 + -10x + x2 = 180 + 25

Combine like terms: 180 + 25 = 205
25 + -10x + x2 = 205

Factor a perfect square on the left side:
(x + -5)(x + -5) = 205

Calculate the square root of the right side: 14.317821063

Break this problem into two subproblems by setting 
(x + -5) equal to 14.317821063 and -14.317821063.


Subproblem 1
x + -5 = 14.317821063

Simplifying
x + -5 = 14.317821063

Reorder the terms:
-5 + x = 14.317821063

Solving
-5 + x = 14.317821063

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = 14.317821063 + 5

Combine like terms: -5 + 5 = 0
0 + x = 14.317821063 + 5
x = 14.317821063 + 5

Combine like terms: 14.317821063 + 5 = 19.317821063
x = 19.317821063

Simplifying
x = 19.317821063


Subproblem 2
x + -5 = -14.317821063

Simplifying
x + -5 = -14.317821063

Reorder the terms:
-5 + x = -14.317821063

Solving
-5 + x = -14.317821063

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = -14.317821063 + 5

Combine like terms: -5 + 5 = 0
0 + x = -14.317821063 + 5
x = -14.317821063 + 5

Combine like terms: -14.317821063 + 5 = -9.317821063
x = -9.317821063

Simplifying
x = -9.317821063


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {19.317821063, -9.317821063}

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