x^2+(5-x)(5-x)=23

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

Simplifying
x2 + (5 + -1x)(5 + -1x) = 23

Multiply (5 + -1x) * (5 + -1x)
x2 + (5(5 + -1x) + -1x * (5 + -1x)) = 23
x2 + ((5 * 5 + -1x * 5) + -1x * (5 + -1x)) = 23
x2 + ((25 + -5x) + -1x * (5 + -1x)) = 23
x2 + (25 + -5x + (5 * -1x + -1x * -1x)) = 23
x2 + (25 + -5x + (-5x + 1x2)) = 23

Combine like terms: -5x + -5x = -10x
x2 + (25 + -10x + 1x2) = 23

Reorder the terms:
25 + -10x + x2 + 1x2 = 23

Combine like terms: x2 + 1x2 = 2x2
25 + -10x + 2x2 = 23

Solving
25 + -10x + 2x2 = 23

Solving for variable 'x'.

Reorder the terms:
25 + -23 + -10x + 2x2 = 23 + -23

Combine like terms: 25 + -23 = 2
2 + -10x + 2x2 = 23 + -23

Combine like terms: 23 + -23 = 0
2 + -10x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + -5x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(1 + -5x + x2)' equal to zero and attempt to solve:

Simplifying
1 + -5x + x2 = 0

Solving
1 + -5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -5x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + -5x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5x + x2 = 0 + -1
-5x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-5x + x2 = -1

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 = -1 + 6.25

Reorder the terms:
6.25 + -5x + x2 = -1 + 6.25

Combine like terms: -1 + 6.25 = 5.25
6.25 + -5x + x2 = 5.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 5.25

Calculate the square root of the right side: 2.291287847

Break this problem into two subproblems by setting 
(x + -2.5) equal to 2.291287847 and -2.291287847.

Subproblem 1
x + -2.5 = 2.291287847

Simplifying
x + -2.5 = 2.291287847

Reorder the terms:
-2.5 + x = 2.291287847

Solving
-2.5 + x = 2.291287847

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 = 2.291287847 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 2.291287847 + 2.5
x = 2.291287847 + 2.5

Combine like terms: 2.291287847 + 2.5 = 4.791287847
x = 4.791287847

Simplifying
x = 4.791287847

Subproblem 2
x + -2.5 = -2.291287847

Simplifying
x + -2.5 = -2.291287847

Reorder the terms:
-2.5 + x = -2.291287847

Solving
-2.5 + x = -2.291287847

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 = -2.291287847 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -2.291287847 + 2.5
x = -2.291287847 + 2.5

Combine like terms: -2.291287847 + 2.5 = 0.208712153
x = 0.208712153

Simplifying
x = 0.208712153

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.791287847, 0.208712153}
Solution
x = {4.791287847, 0.208712153}