(x-10)x=90

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Solution for (x-10)x=90 equation: 


Simplifying
(x + -10) * x = 90

Reorder the terms:
(-10 + x) * x = 90

Reorder the terms for easier multiplication:
x(-10 + x) = 90
(-10 * x + x * x) = 90
(-10x + x2) = 90

Solving
-10x + x2 = 90

Solving for variable 'x'.

Reorder the terms:
-90 + -10x + x2 = 90 + -90

Combine like terms: 90 + -90 = 0
-90 + -10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '90' to each side of the equation.
-90 + -10x + 90 + x2 = 0 + 90

Reorder the terms:
-90 + 90 + -10x + x2 = 0 + 90

Combine like terms: -90 + 90 = 0
0 + -10x + x2 = 0 + 90
-10x + x2 = 0 + 90

Combine like terms: 0 + 90 = 90
-10x + x2 = 90

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 = 90 + 25

Reorder the terms:
25 + -10x + x2 = 90 + 25

Combine like terms: 90 + 25 = 115
25 + -10x + x2 = 115

Factor a perfect square on the left side:
(x + -5)(x + -5) = 115

Calculate the square root of the right side: 10.723805295

Break this problem into two subproblems by setting 
(x + -5) equal to 10.723805295 and -10.723805295.


Subproblem 1
x + -5 = 10.723805295

Simplifying
x + -5 = 10.723805295

Reorder the terms:
-5 + x = 10.723805295

Solving
-5 + x = 10.723805295

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 = 10.723805295 + 5

Combine like terms: -5 + 5 = 0
0 + x = 10.723805295 + 5
x = 10.723805295 + 5

Combine like terms: 10.723805295 + 5 = 15.723805295
x = 15.723805295

Simplifying
x = 15.723805295


Subproblem 2
x + -5 = -10.723805295

Simplifying
x + -5 = -10.723805295

Reorder the terms:
-5 + x = -10.723805295

Solving
-5 + x = -10.723805295

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 = -10.723805295 + 5

Combine like terms: -5 + 5 = 0
0 + x = -10.723805295 + 5
x = -10.723805295 + 5

Combine like terms: -10.723805295 + 5 = -5.723805295
x = -5.723805295

Simplifying
x = -5.723805295


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15.723805295, -5.723805295}

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