(w+1)(w+1)=32

Solution for (w+1)(w+1)=32 equation:

Simplifying
(w + 1)(w + 1) = 32

Reorder the terms:
(1 + w)(w + 1) = 32

Reorder the terms:
(1 + w)(1 + w) = 32

Multiply (1 + w) * (1 + w)
(1(1 + w) + w(1 + w)) = 32
((1 * 1 + w * 1) + w(1 + w)) = 32
((1 + 1w) + w(1 + w)) = 32
(1 + 1w + (1 * w + w * w)) = 32
(1 + 1w + (1w + w2)) = 32

Combine like terms: 1w + 1w = 2w
(1 + 2w + w2) = 32

Solving
1 + 2w + w2 = 32

Solving for variable 'w'.

Reorder the terms:
1 + -32 + 2w + w2 = 32 + -32

Combine like terms: 1 + -32 = -31
-31 + 2w + w2 = 32 + -32

Combine like terms: 32 + -32 = 0
-31 + 2w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '31' to each side of the equation.
-31 + 2w + 31 + w2 = 0 + 31

Reorder the terms:
-31 + 31 + 2w + w2 = 0 + 31

Combine like terms: -31 + 31 = 0
0 + 2w + w2 = 0 + 31
2w + w2 = 0 + 31

Combine like terms: 0 + 31 = 31
2w + w2 = 31

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

Add '1' to each side of the equation.
2w + 1 + w2 = 31 + 1

Reorder the terms:
1 + 2w + w2 = 31 + 1

Combine like terms: 31 + 1 = 32
1 + 2w + w2 = 32

Factor a perfect square on the left side:
(w + 1)(w + 1) = 32

Calculate the square root of the right side: 5.656854249

Break this problem into two subproblems by setting 
(w + 1) equal to 5.656854249 and -5.656854249.

Subproblem 1
w + 1 = 5.656854249

Simplifying
w + 1 = 5.656854249

Reorder the terms:
1 + w = 5.656854249

Solving
1 + w = 5.656854249

Solving for variable 'w'.

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

Add '-1' to each side of the equation.
1 + -1 + w = 5.656854249 + -1

Combine like terms: 1 + -1 = 0
0 + w = 5.656854249 + -1
w = 5.656854249 + -1

Combine like terms: 5.656854249 + -1 = 4.656854249
w = 4.656854249

Simplifying
w = 4.656854249

Subproblem 2
w + 1 = -5.656854249

Simplifying
w + 1 = -5.656854249

Reorder the terms:
1 + w = -5.656854249

Solving
1 + w = -5.656854249

Solving for variable 'w'.

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

Add '-1' to each side of the equation.
1 + -1 + w = -5.656854249 + -1

Combine like terms: 1 + -1 = 0
0 + w = -5.656854249 + -1
w = -5.656854249 + -1

Combine like terms: -5.656854249 + -1 = -6.656854249
w = -6.656854249

Simplifying
w = -6.656854249

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {4.656854249, -6.656854249}