x(x+10)=180

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Solution for x(x+10)=180 equation: 


Simplifying
x(x + 10) = 180

Reorder the terms:
x(10 + x) = 180
(10 * x + x * x) = 180
(10x + x2) = 180

Solving
10x + x2 = 180

Solving for variable 'x'.

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

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

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 = 9.317821063
x = 9.317821063

Simplifying
x = 9.317821063


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 = -19.317821063
x = -19.317821063

Simplifying
x = -19.317821063


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

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