w^2+4w-124=0

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Solution for w^2+4w-124=0 equation:


Simplifying
w2 + 4w + -124 = 0

Reorder the terms:
-124 + 4w + w2 = 0

Solving
-124 + 4w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '124' to each side of the equation.
-124 + 4w + 124 + w2 = 0 + 124

Reorder the terms:
-124 + 124 + 4w + w2 = 0 + 124

Combine like terms: -124 + 124 = 0
0 + 4w + w2 = 0 + 124
4w + w2 = 0 + 124

Combine like terms: 0 + 124 = 124
4w + w2 = 124

The w term is 4w.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4w + 4 + w2 = 124 + 4

Reorder the terms:
4 + 4w + w2 = 124 + 4

Combine like terms: 124 + 4 = 128
4 + 4w + w2 = 128

Factor a perfect square on the left side:
(w + 2)(w + 2) = 128

Calculate the square root of the right side: 11.313708499

Break this problem into two subproblems by setting 
(w + 2) equal to 11.313708499 and -11.313708499.

Subproblem 1

w + 2 = 11.313708499 Simplifying w + 2 = 11.313708499 Reorder the terms: 2 + w = 11.313708499 Solving 2 + w = 11.313708499 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + w = 11.313708499 + -2 Combine like terms: 2 + -2 = 0 0 + w = 11.313708499 + -2 w = 11.313708499 + -2 Combine like terms: 11.313708499 + -2 = 9.313708499 w = 9.313708499 Simplifying w = 9.313708499

Subproblem 2

w + 2 = -11.313708499 Simplifying w + 2 = -11.313708499 Reorder the terms: 2 + w = -11.313708499 Solving 2 + w = -11.313708499 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + w = -11.313708499 + -2 Combine like terms: 2 + -2 = 0 0 + w = -11.313708499 + -2 w = -11.313708499 + -2 Combine like terms: -11.313708499 + -2 = -13.313708499 w = -13.313708499 Simplifying w = -13.313708499

Solution

The solution to the problem is based on the solutions from the subproblems. w = {9.313708499, -13.313708499}

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