(x-1)(x+1)=(x+23)+(x+25)

Solution for (x-1)(x+1)=(x+23)+(x+25) equation:

Simplifying
(x + -1)(x + 1) = (x + 23) + (x + 25)

Reorder the terms:
(-1 + x)(x + 1) = (x + 23) + (x + 25)

Reorder the terms:
(-1 + x)(1 + x) = (x + 23) + (x + 25)

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

Combine like terms: -1x + 1x = 0
(-1 + 0 + x2) = (x + 23) + (x + 25)
(-1 + x2) = (x + 23) + (x + 25)

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

Remove parenthesis around (23 + x)
-1 + x2 = 23 + x + (x + 25)

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

Remove parenthesis around (25 + x)
-1 + x2 = 23 + x + 25 + x

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

Combine like terms: 23 + 25 = 48
-1 + x2 = 48 + x + x

Combine like terms: x + x = 2x
-1 + x2 = 48 + 2x

Solving
-1 + x2 = 48 + 2x

Solving for variable 'x'.

Reorder the terms:
-1 + -48 + -2x + x2 = 48 + 2x + -48 + -2x

Combine like terms: -1 + -48 = -49
-49 + -2x + x2 = 48 + 2x + -48 + -2x

Reorder the terms:
-49 + -2x + x2 = 48 + -48 + 2x + -2x

Combine like terms: 48 + -48 = 0
-49 + -2x + x2 = 0 + 2x + -2x
-49 + -2x + x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-49 + -2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '49' to each side of the equation.
-49 + -2x + 49 + x2 = 0 + 49

Reorder the terms:
-49 + 49 + -2x + x2 = 0 + 49

Combine like terms: -49 + 49 = 0
0 + -2x + x2 = 0 + 49
-2x + x2 = 0 + 49

Combine like terms: 0 + 49 = 49
-2x + x2 = 49

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 49 + 1

Reorder the terms:
1 + -2x + x2 = 49 + 1

Combine like terms: 49 + 1 = 50
1 + -2x + x2 = 50

Factor a perfect square on the left side:
(x + -1)(x + -1) = 50

Calculate the square root of the right side: 7.071067812

Break this problem into two subproblems by setting 
(x + -1) equal to 7.071067812 and -7.071067812.

Subproblem 1
x + -1 = 7.071067812

Simplifying
x + -1 = 7.071067812

Reorder the terms:
-1 + x = 7.071067812

Solving
-1 + x = 7.071067812

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 7.071067812 + 1

Combine like terms: -1 + 1 = 0
0 + x = 7.071067812 + 1
x = 7.071067812 + 1

Combine like terms: 7.071067812 + 1 = 8.071067812
x = 8.071067812

Simplifying
x = 8.071067812

Subproblem 2
x + -1 = -7.071067812

Simplifying
x + -1 = -7.071067812

Reorder the terms:
-1 + x = -7.071067812

Solving
-1 + x = -7.071067812

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -7.071067812 + 1

Combine like terms: -1 + 1 = 0
0 + x = -7.071067812 + 1
x = -7.071067812 + 1

Combine like terms: -7.071067812 + 1 = -6.071067812
x = -6.071067812

Simplifying
x = -6.071067812

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.071067812, -6.071067812}