(10+x)(12+x)=180

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Solution for (10+x)(12+x)=180 equation: 


Simplifying
(10 + x)(12 + x) = 180

Multiply (10 + x) * (12 + x)
(10(12 + x) + x(12 + x)) = 180
((12 * 10 + x * 10) + x(12 + x)) = 180
((120 + 10x) + x(12 + x)) = 180
(120 + 10x + (12 * x + x * x)) = 180
(120 + 10x + (12x + x2)) = 180

Combine like terms: 10x + 12x = 22x
(120 + 22x + x2) = 180

Solving
120 + 22x + x2 = 180

Solving for variable 'x'.

Reorder the terms:
120 + -180 + 22x + x2 = 180 + -180

Combine like terms: 120 + -180 = -60
-60 + 22x + x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-60 + 22x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '60' to each side of the equation.
-60 + 22x + 60 + x2 = 0 + 60

Reorder the terms:
-60 + 60 + 22x + x2 = 0 + 60

Combine like terms: -60 + 60 = 0
0 + 22x + x2 = 0 + 60
22x + x2 = 0 + 60

Combine like terms: 0 + 60 = 60
22x + x2 = 60

The x term is 22x.  Take half its coefficient (11).
Square it (121) and add it to both sides.

Add '121' to each side of the equation.
22x + 121 + x2 = 60 + 121

Reorder the terms:
121 + 22x + x2 = 60 + 121

Combine like terms: 60 + 121 = 181
121 + 22x + x2 = 181

Factor a perfect square on the left side:
(x + 11)(x + 11) = 181

Calculate the square root of the right side: 13.453624047

Break this problem into two subproblems by setting 
(x + 11) equal to 13.453624047 and -13.453624047.


Subproblem 1
x + 11 = 13.453624047

Simplifying
x + 11 = 13.453624047

Reorder the terms:
11 + x = 13.453624047

Solving
11 + x = 13.453624047

Solving for variable 'x'.

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

Add '-11' to each side of the equation.
11 + -11 + x = 13.453624047 + -11

Combine like terms: 11 + -11 = 0
0 + x = 13.453624047 + -11
x = 13.453624047 + -11

Combine like terms: 13.453624047 + -11 = 2.453624047
x = 2.453624047

Simplifying
x = 2.453624047


Subproblem 2
x + 11 = -13.453624047

Simplifying
x + 11 = -13.453624047

Reorder the terms:
11 + x = -13.453624047

Solving
11 + x = -13.453624047

Solving for variable 'x'.

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

Add '-11' to each side of the equation.
11 + -11 + x = -13.453624047 + -11

Combine like terms: 11 + -11 = 0
0 + x = -13.453624047 + -11
x = -13.453624047 + -11

Combine like terms: -13.453624047 + -11 = -24.453624047
x = -24.453624047

Simplifying
x = -24.453624047


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.453624047, -24.453624047}

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