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

Solution for 2(x+1)(x+1)=24 equation:

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

Reorder the terms:
2(1 + x)(x + 1) = 24

Reorder the terms:
2(1 + x)(1 + x) = 24

Multiply (1 + x) * (1 + x)
2(1(1 + x) + x(1 + x)) = 24
2((1 * 1 + x * 1) + x(1 + x)) = 24
2((1 + 1x) + x(1 + x)) = 24
2(1 + 1x + (1 * x + x * x)) = 24
2(1 + 1x + (1x + x2)) = 24

Combine like terms: 1x + 1x = 2x
2(1 + 2x + x2) = 24
(1 * 2 + 2x * 2 + x2 * 2) = 24
(2 + 4x + 2x2) = 24

Solving
2 + 4x + 2x2 = 24

Solving for variable 'x'.

Reorder the terms:
2 + -24 + 4x + 2x2 = 24 + -24

Combine like terms: 2 + -24 = -22
-22 + 4x + 2x2 = 24 + -24

Combine like terms: 24 + -24 = 0
-22 + 4x + 2x2 = 0

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

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

Simplifying
-11 + 2x + x2 = 0

Solving
-11 + 2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + 2x + 11 + x2 = 0 + 11

Reorder the terms:
-11 + 11 + 2x + x2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + 2x + x2 = 0 + 11
2x + x2 = 0 + 11

Combine like terms: 0 + 11 = 11
2x + x2 = 11

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 = 11 + 1

Reorder the terms:
1 + 2x + x2 = 11 + 1

Combine like terms: 11 + 1 = 12
1 + 2x + x2 = 12

Factor a perfect square on the left side:
(x + 1)(x + 1) = 12

Calculate the square root of the right side: 3.464101615

Break this problem into two subproblems by setting 
(x + 1) equal to 3.464101615 and -3.464101615.

Subproblem 1
x + 1 = 3.464101615

Simplifying
x + 1 = 3.464101615

Reorder the terms:
1 + x = 3.464101615

Solving
1 + x = 3.464101615

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 = 3.464101615 + -1

Combine like terms: 1 + -1 = 0
0 + x = 3.464101615 + -1
x = 3.464101615 + -1

Combine like terms: 3.464101615 + -1 = 2.464101615
x = 2.464101615

Simplifying
x = 2.464101615

Subproblem 2
x + 1 = -3.464101615

Simplifying
x + 1 = -3.464101615

Reorder the terms:
1 + x = -3.464101615

Solving
1 + x = -3.464101615

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 = -3.464101615 + -1

Combine like terms: 1 + -1 = 0
0 + x = -3.464101615 + -1
x = -3.464101615 + -1

Combine like terms: -3.464101615 + -1 = -4.464101615
x = -4.464101615

Simplifying
x = -4.464101615

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.464101615, -4.464101615}
Solution
x = {2.464101615, -4.464101615}