2(x+1)(x+1)=40

Solution for 2(x+1)(x+1)=40 equation:

Simplifying
2(x + 1)(x + 1) = 40

Reorder the terms:
2(1 + x)(x + 1) = 40

Reorder the terms:
2(1 + x)(1 + x) = 40

Multiply (1 + x) * (1 + x)
2(1(1 + x) + x(1 + x)) = 40
2((1 * 1 + x * 1) + x(1 + x)) = 40
2((1 + 1x) + x(1 + x)) = 40
2(1 + 1x + (1 * x + x * x)) = 40
2(1 + 1x + (1x + x2)) = 40

Combine like terms: 1x + 1x = 2x
2(1 + 2x + x2) = 40
(1 * 2 + 2x * 2 + x2 * 2) = 40
(2 + 4x + 2x2) = 40

Solving
2 + 4x + 2x2 = 40

Solving for variable 'x'.

Reorder the terms:
2 + -40 + 4x + 2x2 = 40 + -40

Combine like terms: 2 + -40 = -38
-38 + 4x + 2x2 = 40 + -40

Combine like terms: 40 + -40 = 0
-38 + 4x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-19 + 2x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-19 + 2x + x2)' equal to zero and attempt to solve:

Simplifying
-19 + 2x + x2 = 0

Solving
-19 + 2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '19' to each side of the equation.
-19 + 2x + 19 + x2 = 0 + 19

Reorder the terms:
-19 + 19 + 2x + x2 = 0 + 19

Combine like terms: -19 + 19 = 0
0 + 2x + x2 = 0 + 19
2x + x2 = 0 + 19

Combine like terms: 0 + 19 = 19
2x + x2 = 19

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 = 19 + 1

Reorder the terms:
1 + 2x + x2 = 19 + 1

Combine like terms: 19 + 1 = 20
1 + 2x + x2 = 20

Factor a perfect square on the left side:
(x + 1)(x + 1) = 20

Calculate the square root of the right side: 4.472135955

Break this problem into two subproblems by setting 
(x + 1) equal to 4.472135955 and -4.472135955.

Subproblem 1
x + 1 = 4.472135955

Simplifying
x + 1 = 4.472135955

Reorder the terms:
1 + x = 4.472135955

Solving
1 + x = 4.472135955

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 = 4.472135955 + -1

Combine like terms: 1 + -1 = 0
0 + x = 4.472135955 + -1
x = 4.472135955 + -1

Combine like terms: 4.472135955 + -1 = 3.472135955
x = 3.472135955

Simplifying
x = 3.472135955

Subproblem 2
x + 1 = -4.472135955

Simplifying
x + 1 = -4.472135955

Reorder the terms:
1 + x = -4.472135955

Solving
1 + x = -4.472135955

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 = -4.472135955 + -1

Combine like terms: 1 + -1 = 0
0 + x = -4.472135955 + -1
x = -4.472135955 + -1

Combine like terms: -4.472135955 + -1 = -5.472135955
x = -5.472135955

Simplifying
x = -5.472135955

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.472135955, -5.472135955}
Solution
x = {3.472135955, -5.472135955}