w^2+2w-104=0

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Solution for w^2+2w-104=0 equation:


Simplifying
w2 + 2w + -104 = 0

Reorder the terms:
-104 + 2w + w2 = 0

Solving
-104 + 2w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '104' to each side of the equation.
-104 + 2w + 104 + w2 = 0 + 104

Reorder the terms:
-104 + 104 + 2w + w2 = 0 + 104

Combine like terms: -104 + 104 = 0
0 + 2w + w2 = 0 + 104
2w + w2 = 0 + 104

Combine like terms: 0 + 104 = 104
2w + w2 = 104

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 = 104 + 1

Reorder the terms:
1 + 2w + w2 = 104 + 1

Combine like terms: 104 + 1 = 105
1 + 2w + w2 = 105

Factor a perfect square on the left side:
(w + 1)(w + 1) = 105

Calculate the square root of the right side: 10.246950766

Break this problem into two subproblems by setting 
(w + 1) equal to 10.246950766 and -10.246950766.

Subproblem 1

w + 1 = 10.246950766 Simplifying w + 1 = 10.246950766 Reorder the terms: 1 + w = 10.246950766 Solving 1 + w = 10.246950766 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 = 10.246950766 + -1 Combine like terms: 1 + -1 = 0 0 + w = 10.246950766 + -1 w = 10.246950766 + -1 Combine like terms: 10.246950766 + -1 = 9.246950766 w = 9.246950766 Simplifying w = 9.246950766

Subproblem 2

w + 1 = -10.246950766 Simplifying w + 1 = -10.246950766 Reorder the terms: 1 + w = -10.246950766 Solving 1 + w = -10.246950766 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 = -10.246950766 + -1 Combine like terms: 1 + -1 = 0 0 + w = -10.246950766 + -1 w = -10.246950766 + -1 Combine like terms: -10.246950766 + -1 = -11.246950766 w = -11.246950766 Simplifying w = -11.246950766

Solution

The solution to the problem is based on the solutions from the subproblems. w = {9.246950766, -11.246950766}

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