x(x-10)=8

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Solution for x(x-10)=8 equation: 


Simplifying
x(x + -10) = 8

Reorder the terms:
x(-10 + x) = 8
(-10 * x + x * x) = 8
(-10x + x2) = 8

Solving
-10x + x2 = 8

Solving for variable 'x'.

Reorder the terms:
-8 + -10x + x2 = 8 + -8

Combine like terms: 8 + -8 = 0
-8 + -10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + -10x + 8 + x2 = 0 + 8

Reorder the terms:
-8 + 8 + -10x + x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -10x + x2 = 0 + 8
-10x + x2 = 0 + 8

Combine like terms: 0 + 8 = 8
-10x + x2 = 8

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 = 8 + 25

Reorder the terms:
25 + -10x + x2 = 8 + 25

Combine like terms: 8 + 25 = 33
25 + -10x + x2 = 33

Factor a perfect square on the left side:
(x + -5)(x + -5) = 33

Calculate the square root of the right side: 5.744562647

Break this problem into two subproblems by setting 
(x + -5) equal to 5.744562647 and -5.744562647.


Subproblem 1
x + -5 = 5.744562647

Simplifying
x + -5 = 5.744562647

Reorder the terms:
-5 + x = 5.744562647

Solving
-5 + x = 5.744562647

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 = 5.744562647 + 5

Combine like terms: -5 + 5 = 0
0 + x = 5.744562647 + 5
x = 5.744562647 + 5

Combine like terms: 5.744562647 + 5 = 10.744562647
x = 10.744562647

Simplifying
x = 10.744562647


Subproblem 2
x + -5 = -5.744562647

Simplifying
x + -5 = -5.744562647

Reorder the terms:
-5 + x = -5.744562647

Solving
-5 + x = -5.744562647

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 = -5.744562647 + 5

Combine like terms: -5 + 5 = 0
0 + x = -5.744562647 + 5
x = -5.744562647 + 5

Combine like terms: -5.744562647 + 5 = -0.744562647
x = -0.744562647

Simplifying
x = -0.744562647


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.744562647, -0.744562647}

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