22x-11=(x+5)(x+5)

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Solution for 22x-11=(x+5)(x+5) equation: 


Simplifying
22x + -11 = (x + 5)(x + 5)

Reorder the terms:
-11 + 22x = (x + 5)(x + 5)

Reorder the terms:
-11 + 22x = (5 + x)(x + 5)

Reorder the terms:
-11 + 22x = (5 + x)(5 + x)

Multiply (5 + x) * (5 + x)
-11 + 22x = (5(5 + x) + x(5 + x))
-11 + 22x = ((5 * 5 + x * 5) + x(5 + x))
-11 + 22x = ((25 + 5x) + x(5 + x))
-11 + 22x = (25 + 5x + (5 * x + x * x))
-11 + 22x = (25 + 5x + (5x + x2))

Combine like terms: 5x + 5x = 10x
-11 + 22x = (25 + 10x + x2)

Solving
-11 + 22x = 25 + 10x + x2

Solving for variable 'x'.

Reorder the terms:
-11 + -25 + 22x + -10x + -1x2 = 25 + 10x + x2 + -25 + -10x + -1x2

Combine like terms: -11 + -25 = -36
-36 + 22x + -10x + -1x2 = 25 + 10x + x2 + -25 + -10x + -1x2

Combine like terms: 22x + -10x = 12x
-36 + 12x + -1x2 = 25 + 10x + x2 + -25 + -10x + -1x2

Reorder the terms:
-36 + 12x + -1x2 = 25 + -25 + 10x + -10x + x2 + -1x2

Combine like terms: 25 + -25 = 0
-36 + 12x + -1x2 = 0 + 10x + -10x + x2 + -1x2
-36 + 12x + -1x2 = 10x + -10x + x2 + -1x2

Combine like terms: 10x + -10x = 0
-36 + 12x + -1x2 = 0 + x2 + -1x2
-36 + 12x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-36 + 12x + -1x2 = 0

Factor a trinomial.
(-6 + x)(6 + -1x) = 0


Subproblem 1
Set the factor '(-6 + x)' equal to zero and attempt to solve:

Simplifying
-6 + x = 0

Solving
-6 + x = 0

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

Add '6' to each side of the equation.
-6 + 6 + x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + x = 0 + 6
x = 0 + 6

Combine like terms: 0 + 6 = 6
x = 6

Simplifying
x = 6

Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {6, 6}

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