(x+1)(x+1)=24

Solution for (x+1)(x+1)=24 equation:

Simplifying
(x + 1)(x + 1) = 24

Reorder the terms:
(1 + x)(x + 1) = 24

Reorder the terms:
(1 + x)(1 + x) = 24

Multiply (1 + x) * (1 + x)
(1(1 + x) + x(1 + x)) = 24
((1 * 1 + x * 1) + x(1 + x)) = 24
((1 + 1x) + x(1 + x)) = 24
(1 + 1x + (1 * x + x * x)) = 24
(1 + 1x + (1x + x2)) = 24

Combine like terms: 1x + 1x = 2x
(1 + 2x + x2) = 24

Solving
1 + 2x + x2 = 24

Solving for variable 'x'.

Reorder the terms:
1 + -24 + 2x + x2 = 24 + -24

Combine like terms: 1 + -24 = -23
-23 + 2x + x2 = 24 + -24

Combine like terms: 24 + -24 = 0
-23 + 2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '23' to each side of the equation.
-23 + 2x + 23 + x2 = 0 + 23

Reorder the terms:
-23 + 23 + 2x + x2 = 0 + 23

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

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

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 = 23 + 1

Reorder the terms:
1 + 2x + x2 = 23 + 1

Combine like terms: 23 + 1 = 24
1 + 2x + x2 = 24

Factor a perfect square on the left side:
(x + 1)(x + 1) = 24

Calculate the square root of the right side: 4.898979486

Break this problem into two subproblems by setting 
(x + 1) equal to 4.898979486 and -4.898979486.

Subproblem 1
x + 1 = 4.898979486

Simplifying
x + 1 = 4.898979486

Reorder the terms:
1 + x = 4.898979486

Solving
1 + x = 4.898979486

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 = 4.898979486 + -1

Combine like terms: 1 + -1 = 0
0 + x = 4.898979486 + -1
x = 4.898979486 + -1

Combine like terms: 4.898979486 + -1 = 3.898979486
x = 3.898979486

Simplifying
x = 3.898979486

Subproblem 2
x + 1 = -4.898979486

Simplifying
x + 1 = -4.898979486

Reorder the terms:
1 + x = -4.898979486

Solving
1 + x = -4.898979486

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 = -4.898979486 + -1

Combine like terms: 1 + -1 = 0
0 + x = -4.898979486 + -1
x = -4.898979486 + -1

Combine like terms: -4.898979486 + -1 = -5.898979486
x = -5.898979486

Simplifying
x = -5.898979486

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.898979486, -5.898979486}