x(x+20)90=180

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Solution for x(x+20)90=180 equation: 


Simplifying
x(x + 20) * 90 = 180

Reorder the terms:
x(20 + x) * 90 = 180

Reorder the terms for easier multiplication:
90x(20 + x) = 180
(20 * 90x + x * 90x) = 180
(1800x + 90x2) = 180

Solving
1800x + 90x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + 1800x + 90x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 1800x + 90x2 = 0

Factor out the Greatest Common Factor (GCF), '90'.
90(-2 + 20x + x2) = 0

Ignore the factor 90.

Subproblem 1
Set the factor '(-2 + 20x + x2)' equal to zero and attempt to solve:

Simplifying
-2 + 20x + x2 = 0

Solving
-2 + 20x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 20x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + 20x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 20x + x2 = 0 + 2
20x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
20x + x2 = 2

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 = 2 + 100

Reorder the terms:
100 + 20x + x2 = 2 + 100

Combine like terms: 2 + 100 = 102
100 + 20x + x2 = 102

Factor a perfect square on the left side:
(x + 10)(x + 10) = 102

Calculate the square root of the right side: 10.099504938

Break this problem into two subproblems by setting 
(x + 10) equal to 10.099504938 and -10.099504938.


Subproblem 1
x + 10 = 10.099504938

Simplifying
x + 10 = 10.099504938

Reorder the terms:
10 + x = 10.099504938

Solving
10 + x = 10.099504938

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 = 10.099504938 + -10

Combine like terms: 10 + -10 = 0
0 + x = 10.099504938 + -10
x = 10.099504938 + -10

Combine like terms: 10.099504938 + -10 = 0.099504938
x = 0.099504938

Simplifying
x = 0.099504938


Subproblem 2
x + 10 = -10.099504938

Simplifying
x + 10 = -10.099504938

Reorder the terms:
10 + x = -10.099504938

Solving
10 + x = -10.099504938

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 = -10.099504938 + -10

Combine like terms: 10 + -10 = 0
0 + x = -10.099504938 + -10
x = -10.099504938 + -10

Combine like terms: -10.099504938 + -10 = -20.099504938
x = -20.099504938

Simplifying
x = -20.099504938


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.099504938, -20.099504938}
Solution
x = {0.099504938, -20.099504938}

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