x(x+20)=180

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Solution for x(x+20)=180 equation: 


Simplifying
x(x + 20) = 180

Reorder the terms:
x(20 + x) = 180
(20 * x + x * x) = 180
(20x + x2) = 180

Solving
20x + x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + 20x + x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 20x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '180' to each side of the equation.
-180 + 20x + 180 + x2 = 0 + 180

Reorder the terms:
-180 + 180 + 20x + x2 = 0 + 180

Combine like terms: -180 + 180 = 0
0 + 20x + x2 = 0 + 180
20x + x2 = 0 + 180

Combine like terms: 0 + 180 = 180
20x + x2 = 180

The x term is 20x.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20x + 100 + x2 = 180 + 100

Reorder the terms:
100 + 20x + x2 = 180 + 100

Combine like terms: 180 + 100 = 280
100 + 20x + x2 = 280

Factor a perfect square on the left side:
(x + 10)(x + 10) = 280

Calculate the square root of the right side: 16.733200531

Break this problem into two subproblems by setting 
(x + 10) equal to 16.733200531 and -16.733200531.


Subproblem 1
x + 10 = 16.733200531

Simplifying
x + 10 = 16.733200531

Reorder the terms:
10 + x = 16.733200531

Solving
10 + x = 16.733200531

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x = 16.733200531 + -10

Combine like terms: 10 + -10 = 0
0 + x = 16.733200531 + -10
x = 16.733200531 + -10

Combine like terms: 16.733200531 + -10 = 6.733200531
x = 6.733200531

Simplifying
x = 6.733200531


Subproblem 2
x + 10 = -16.733200531

Simplifying
x + 10 = -16.733200531

Reorder the terms:
10 + x = -16.733200531

Solving
10 + x = -16.733200531

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x = -16.733200531 + -10

Combine like terms: 10 + -10 = 0
0 + x = -16.733200531 + -10
x = -16.733200531 + -10

Combine like terms: -16.733200531 + -10 = -26.733200531
x = -26.733200531

Simplifying
x = -26.733200531


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.733200531, -26.733200531}

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