20*26=x*(x+22)

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Solution for 20*26=x*(x+22) equation: 


Simplifying
20 * 26 = x(x + 22)

Multiply 20 * 26
520 = x(x + 22)

Reorder the terms:
520 = x(22 + x)
520 = (22 * x + x * x)
520 = (22x + x2)

Solving
520 = 22x + x2

Solving for variable 'x'.

Reorder the terms:
520 + -22x + -1x2 = 22x + -22x + x2 + -1x2

Combine like terms: 22x + -22x = 0
520 + -22x + -1x2 = 0 + x2 + -1x2
520 + -22x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
520 + -22x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-520 + 22x + x2 = 0

Move the constant term to the right:

Add '520' to each side of the equation.
-520 + 22x + 520 + x2 = 0 + 520

Reorder the terms:
-520 + 520 + 22x + x2 = 0 + 520

Combine like terms: -520 + 520 = 0
0 + 22x + x2 = 0 + 520
22x + x2 = 0 + 520

Combine like terms: 0 + 520 = 520
22x + x2 = 520

The x term is 22x.  Take half its coefficient (11).
Square it (121) and add it to both sides.

Add '121' to each side of the equation.
22x + 121 + x2 = 520 + 121

Reorder the terms:
121 + 22x + x2 = 520 + 121

Combine like terms: 520 + 121 = 641
121 + 22x + x2 = 641

Factor a perfect square on the left side:
(x + 11)(x + 11) = 641

Calculate the square root of the right side: 25.317977802

Break this problem into two subproblems by setting 
(x + 11) equal to 25.317977802 and -25.317977802.


Subproblem 1
x + 11 = 25.317977802

Simplifying
x + 11 = 25.317977802

Reorder the terms:
11 + x = 25.317977802

Solving
11 + x = 25.317977802

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-11' to each side of the equation.
11 + -11 + x = 25.317977802 + -11

Combine like terms: 11 + -11 = 0
0 + x = 25.317977802 + -11
x = 25.317977802 + -11

Combine like terms: 25.317977802 + -11 = 14.317977802
x = 14.317977802

Simplifying
x = 14.317977802


Subproblem 2
x + 11 = -25.317977802

Simplifying
x + 11 = -25.317977802

Reorder the terms:
11 + x = -25.317977802

Solving
11 + x = -25.317977802

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-11' to each side of the equation.
11 + -11 + x = -25.317977802 + -11

Combine like terms: 11 + -11 = 0
0 + x = -25.317977802 + -11
x = -25.317977802 + -11

Combine like terms: -25.317977802 + -11 = -36.317977802
x = -36.317977802

Simplifying
x = -36.317977802


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.317977802, -36.317977802}

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