(2x-5)(2x-5)-23=0

Solution for (2x-5)(2x-5)-23=0 equation:

Simplifying
(2x + -5)(2x + -5) + -23 = 0

Reorder the terms:
(-5 + 2x)(2x + -5) + -23 = 0

Reorder the terms:
(-5 + 2x)(-5 + 2x) + -23 = 0

Multiply (-5 + 2x) * (-5 + 2x)
(-5(-5 + 2x) + 2x * (-5 + 2x)) + -23 = 0
((-5 * -5 + 2x * -5) + 2x * (-5 + 2x)) + -23 = 0
((25 + -10x) + 2x * (-5 + 2x)) + -23 = 0
(25 + -10x + (-5 * 2x + 2x * 2x)) + -23 = 0
(25 + -10x + (-10x + 4x2)) + -23 = 0

Combine like terms: -10x + -10x = -20x
(25 + -20x + 4x2) + -23 = 0

Reorder the terms:
25 + -23 + -20x + 4x2 = 0

Combine like terms: 25 + -23 = 2
2 + -20x + 4x2 = 0

Solving
2 + -20x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + -10x + 2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(1 + -10x + 2x2)' equal to zero and attempt to solve:

Simplifying
1 + -10x + 2x2 = 0

Solving
1 + -10x + 2x2 = 0

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

Divide each side by '2'.
0.5 + -5x + x2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + -5x + -0.5 + x2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + -5x + x2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + -5x + x2 = 0 + -0.5
-5x + x2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
-5x + x2 = -0.5

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = -0.5 + 6.25

Reorder the terms:
6.25 + -5x + x2 = -0.5 + 6.25

Combine like terms: -0.5 + 6.25 = 5.75
6.25 + -5x + x2 = 5.75

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 5.75

Calculate the square root of the right side: 2.397915762

Break this problem into two subproblems by setting 
(x + -2.5) equal to 2.397915762 and -2.397915762.

Subproblem 1
x + -2.5 = 2.397915762

Simplifying
x + -2.5 = 2.397915762

Reorder the terms:
-2.5 + x = 2.397915762

Solving
-2.5 + x = 2.397915762

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 2.397915762 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 2.397915762 + 2.5
x = 2.397915762 + 2.5

Combine like terms: 2.397915762 + 2.5 = 4.897915762
x = 4.897915762

Simplifying
x = 4.897915762

Subproblem 2
x + -2.5 = -2.397915762

Simplifying
x + -2.5 = -2.397915762

Reorder the terms:
-2.5 + x = -2.397915762

Solving
-2.5 + x = -2.397915762

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -2.397915762 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -2.397915762 + 2.5
x = -2.397915762 + 2.5

Combine like terms: -2.397915762 + 2.5 = 0.102084238
x = 0.102084238

Simplifying
x = 0.102084238

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.897915762, 0.102084238}
Solution
x = {4.897915762, 0.102084238}