(3+w^2)+(w-1)=104

Solution for (3+w^2)+(w-1)=104 equation:

Simplifying
(3 + w2) + (w + -1) = 104

Remove parenthesis around (3 + w2)
3 + w2 + (w + -1) = 104

Reorder the terms:
3 + w2 + (-1 + w) = 104

Remove parenthesis around (-1 + w)
3 + w2 + -1 + w = 104

Reorder the terms:
3 + -1 + w + w2 = 104

Combine like terms: 3 + -1 = 2
2 + w + w2 = 104

Solving
2 + w + w2 = 104

Solving for variable 'w'.

Reorder the terms:
2 + -104 + w + w2 = 104 + -104

Combine like terms: 2 + -104 = -102
-102 + w + w2 = 104 + -104

Combine like terms: 104 + -104 = 0
-102 + w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '102' to each side of the equation.
-102 + w + 102 + w2 = 0 + 102

Reorder the terms:
-102 + 102 + w + w2 = 0 + 102

Combine like terms: -102 + 102 = 0
0 + w + w2 = 0 + 102
w + w2 = 0 + 102

Combine like terms: 0 + 102 = 102
w + w2 = 102

The w term is w.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
w + 0.25 + w2 = 102 + 0.25

Reorder the terms:
0.25 + w + w2 = 102 + 0.25

Combine like terms: 102 + 0.25 = 102.25
0.25 + w + w2 = 102.25

Factor a perfect square on the left side:
(w + 0.5)(w + 0.5) = 102.25

Calculate the square root of the right side: 10.111874208

Break this problem into two subproblems by setting 
(w + 0.5) equal to 10.111874208 and -10.111874208.

Subproblem 1
w + 0.5 = 10.111874208

Simplifying
w + 0.5 = 10.111874208

Reorder the terms:
0.5 + w = 10.111874208

Solving
0.5 + w = 10.111874208

Solving for variable 'w'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + w = 10.111874208 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + w = 10.111874208 + -0.5
w = 10.111874208 + -0.5

Combine like terms: 10.111874208 + -0.5 = 9.611874208
w = 9.611874208

Simplifying
w = 9.611874208

Subproblem 2
w + 0.5 = -10.111874208

Simplifying
w + 0.5 = -10.111874208

Reorder the terms:
0.5 + w = -10.111874208

Solving
0.5 + w = -10.111874208

Solving for variable 'w'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + w = -10.111874208 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + w = -10.111874208 + -0.5
w = -10.111874208 + -0.5

Combine like terms: -10.111874208 + -0.5 = -10.611874208
w = -10.611874208

Simplifying
w = -10.611874208

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {9.611874208, -10.611874208}