x(x-10)=27

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Solution for x(x-10)=27 equation: 


Simplifying
x(x + -10) = 27

Reorder the terms:
x(-10 + x) = 27
(-10 * x + x * x) = 27
(-10x + x2) = 27

Solving
-10x + x2 = 27

Solving for variable 'x'.

Reorder the terms:
-27 + -10x + x2 = 27 + -27

Combine like terms: 27 + -27 = 0
-27 + -10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '27' to each side of the equation.
-27 + -10x + 27 + x2 = 0 + 27

Reorder the terms:
-27 + 27 + -10x + x2 = 0 + 27

Combine like terms: -27 + 27 = 0
0 + -10x + x2 = 0 + 27
-10x + x2 = 0 + 27

Combine like terms: 0 + 27 = 27
-10x + x2 = 27

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 = 27 + 25

Reorder the terms:
25 + -10x + x2 = 27 + 25

Combine like terms: 27 + 25 = 52
25 + -10x + x2 = 52

Factor a perfect square on the left side:
(x + -5)(x + -5) = 52

Calculate the square root of the right side: 7.211102551

Break this problem into two subproblems by setting 
(x + -5) equal to 7.211102551 and -7.211102551.


Subproblem 1
x + -5 = 7.211102551

Simplifying
x + -5 = 7.211102551

Reorder the terms:
-5 + x = 7.211102551

Solving
-5 + x = 7.211102551

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 = 7.211102551 + 5

Combine like terms: -5 + 5 = 0
0 + x = 7.211102551 + 5
x = 7.211102551 + 5

Combine like terms: 7.211102551 + 5 = 12.211102551
x = 12.211102551

Simplifying
x = 12.211102551


Subproblem 2
x + -5 = -7.211102551

Simplifying
x + -5 = -7.211102551

Reorder the terms:
-5 + x = -7.211102551

Solving
-5 + x = -7.211102551

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 = -7.211102551 + 5

Combine like terms: -5 + 5 = 0
0 + x = -7.211102551 + 5
x = -7.211102551 + 5

Combine like terms: -7.211102551 + 5 = -2.211102551
x = -2.211102551

Simplifying
x = -2.211102551


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.211102551, -2.211102551}

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