x(x-10)=-10

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


Simplifying
x(x + -10) = -10

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

Solving
-10x + x2 = -10

Solving for variable 'x'.

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

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

Begin completing the square.

Move the constant term to the right:

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

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

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

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

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 = -10 + 25

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

Combine like terms: -10 + 25 = 15
25 + -10x + x2 = 15

Factor a perfect square on the left side:
(x + -5)(x + -5) = 15

Calculate the square root of the right side: 3.872983346

Break this problem into two subproblems by setting 
(x + -5) equal to 3.872983346 and -3.872983346.


Subproblem 1
x + -5 = 3.872983346

Simplifying
x + -5 = 3.872983346

Reorder the terms:
-5 + x = 3.872983346

Solving
-5 + x = 3.872983346

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 = 3.872983346 + 5

Combine like terms: -5 + 5 = 0
0 + x = 3.872983346 + 5
x = 3.872983346 + 5

Combine like terms: 3.872983346 + 5 = 8.872983346
x = 8.872983346

Simplifying
x = 8.872983346


Subproblem 2
x + -5 = -3.872983346

Simplifying
x + -5 = -3.872983346

Reorder the terms:
-5 + x = -3.872983346

Solving
-5 + x = -3.872983346

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 = -3.872983346 + 5

Combine like terms: -5 + 5 = 0
0 + x = -3.872983346 + 5
x = -3.872983346 + 5

Combine like terms: -3.872983346 + 5 = 1.127016654
x = 1.127016654

Simplifying
x = 1.127016654


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.872983346, 1.127016654}

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