5x(x-10)=22

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Solution for 5x(x-10)=22 equation: 


Simplifying
5x(x + -10) = 22

Reorder the terms:
5x(-10 + x) = 22
(-10 * 5x + x * 5x) = 22
(-50x + 5x2) = 22

Solving
-50x + 5x2 = 22

Solving for variable 'x'.

Reorder the terms:
-22 + -50x + 5x2 = 22 + -22

Combine like terms: 22 + -22 = 0
-22 + -50x + 5x2 = 0

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
-4.4 + -10x + x2 = 0

Move the constant term to the right:

Add '4.4' to each side of the equation.
-4.4 + -10x + 4.4 + x2 = 0 + 4.4

Reorder the terms:
-4.4 + 4.4 + -10x + x2 = 0 + 4.4

Combine like terms: -4.4 + 4.4 = 0.0
0.0 + -10x + x2 = 0 + 4.4
-10x + x2 = 0 + 4.4

Combine like terms: 0 + 4.4 = 4.4
-10x + x2 = 4.4

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 = 4.4 + 25

Reorder the terms:
25 + -10x + x2 = 4.4 + 25

Combine like terms: 4.4 + 25 = 29.4
25 + -10x + x2 = 29.4

Factor a perfect square on the left side:
(x + -5)(x + -5) = 29.4

Calculate the square root of the right side: 5.422176685

Break this problem into two subproblems by setting 
(x + -5) equal to 5.422176685 and -5.422176685.


Subproblem 1
x + -5 = 5.422176685

Simplifying
x + -5 = 5.422176685

Reorder the terms:
-5 + x = 5.422176685

Solving
-5 + x = 5.422176685

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 = 5.422176685 + 5

Combine like terms: -5 + 5 = 0
0 + x = 5.422176685 + 5
x = 5.422176685 + 5

Combine like terms: 5.422176685 + 5 = 10.422176685
x = 10.422176685

Simplifying
x = 10.422176685


Subproblem 2
x + -5 = -5.422176685

Simplifying
x + -5 = -5.422176685

Reorder the terms:
-5 + x = -5.422176685

Solving
-5 + x = -5.422176685

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 = -5.422176685 + 5

Combine like terms: -5 + 5 = 0
0 + x = -5.422176685 + 5
x = -5.422176685 + 5

Combine like terms: -5.422176685 + 5 = -0.422176685
x = -0.422176685

Simplifying
x = -0.422176685


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.422176685, -0.422176685}

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