23x^2=(x+11)(x+11)

Solution for 23x^2=(x+11)(x+11) equation:

Simplifying
23x2 = (x + 11)(x + 11)

Reorder the terms:
23x2 = (11 + x)(x + 11)

Reorder the terms:
23x2 = (11 + x)(11 + x)

Multiply (11 + x) * (11 + x)
23x2 = (11(11 + x) + x(11 + x))
23x2 = ((11 * 11 + x * 11) + x(11 + x))
23x2 = ((121 + 11x) + x(11 + x))
23x2 = (121 + 11x + (11 * x + x * x))
23x2 = (121 + 11x + (11x + x2))

Combine like terms: 11x + 11x = 22x
23x2 = (121 + 22x + x2)

Solving
23x2 = 121 + 22x + x2

Solving for variable 'x'.

Reorder the terms:
-121 + -22x + 23x2 + -1x2 = 121 + 22x + x2 + -121 + -22x + -1x2

Combine like terms: 23x2 + -1x2 = 22x2
-121 + -22x + 22x2 = 121 + 22x + x2 + -121 + -22x + -1x2

Reorder the terms:
-121 + -22x + 22x2 = 121 + -121 + 22x + -22x + x2 + -1x2

Combine like terms: 121 + -121 = 0
-121 + -22x + 22x2 = 0 + 22x + -22x + x2 + -1x2
-121 + -22x + 22x2 = 22x + -22x + x2 + -1x2

Combine like terms: 22x + -22x = 0
-121 + -22x + 22x2 = 0 + x2 + -1x2
-121 + -22x + 22x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-121 + -22x + 22x2 = 0

Factor out the Greatest Common Factor (GCF), '11'.
11(-11 + -2x + 2x2) = 0

Ignore the factor 11.
Subproblem 1
Set the factor '(-11 + -2x + 2x2)' equal to zero and attempt to solve:

Simplifying
-11 + -2x + 2x2 = 0

Solving
-11 + -2x + 2x2 = 0

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

Divide each side by '2'.
-5.5 + -1x + x2 = 0

Move the constant term to the right:

Add '5.5' to each side of the equation.
-5.5 + -1x + 5.5 + x2 = 0 + 5.5

Reorder the terms:
-5.5 + 5.5 + -1x + x2 = 0 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + -1x + x2 = 0 + 5.5
-1x + x2 = 0 + 5.5

Combine like terms: 0 + 5.5 = 5.5
-1x + x2 = 5.5

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 5.5 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 5.5 + 0.25

Combine like terms: 5.5 + 0.25 = 5.75
0.25 + -1x + x2 = 5.75

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 5.75

Calculate the square root of the right side: 2.397915762

Break this problem into two subproblems by setting 
(x + -0.5) equal to 2.397915762 and -2.397915762.

Subproblem 1
x + -0.5 = 2.397915762

Simplifying
x + -0.5 = 2.397915762

Reorder the terms:
-0.5 + x = 2.397915762

Solving
-0.5 + x = 2.397915762

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = 2.397915762 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 2.397915762 + 0.5
x = 2.397915762 + 0.5

Combine like terms: 2.397915762 + 0.5 = 2.897915762
x = 2.897915762

Simplifying
x = 2.897915762

Subproblem 2
x + -0.5 = -2.397915762

Simplifying
x + -0.5 = -2.397915762

Reorder the terms:
-0.5 + x = -2.397915762

Solving
-0.5 + x = -2.397915762

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = -2.397915762 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -2.397915762 + 0.5
x = -2.397915762 + 0.5

Combine like terms: -2.397915762 + 0.5 = -1.897915762
x = -1.897915762

Simplifying
x = -1.897915762

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.897915762, -1.897915762}
Solution
x = {2.897915762, -1.897915762}