w^2+8w-4=0

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Solution for w^2+8w-4=0 equation:


Simplifying
w2 + 8w + -4 = 0

Reorder the terms:
-4 + 8w + w2 = 0

Solving
-4 + 8w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 8w + 4 + w2 = 0 + 4

Reorder the terms:
-4 + 4 + 8w + w2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 8w + w2 = 0 + 4
8w + w2 = 0 + 4

Combine like terms: 0 + 4 = 4
8w + w2 = 4

The w term is 8w.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8w + 16 + w2 = 4 + 16

Reorder the terms:
16 + 8w + w2 = 4 + 16

Combine like terms: 4 + 16 = 20
16 + 8w + w2 = 20

Factor a perfect square on the left side:
(w + 4)(w + 4) = 20

Calculate the square root of the right side: 4.472135955

Break this problem into two subproblems by setting 
(w + 4) equal to 4.472135955 and -4.472135955.

Subproblem 1

w + 4 = 4.472135955 Simplifying w + 4 = 4.472135955 Reorder the terms: 4 + w = 4.472135955 Solving 4 + w = 4.472135955 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + w = 4.472135955 + -4 Combine like terms: 4 + -4 = 0 0 + w = 4.472135955 + -4 w = 4.472135955 + -4 Combine like terms: 4.472135955 + -4 = 0.472135955 w = 0.472135955 Simplifying w = 0.472135955

Subproblem 2

w + 4 = -4.472135955 Simplifying w + 4 = -4.472135955 Reorder the terms: 4 + w = -4.472135955 Solving 4 + w = -4.472135955 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + w = -4.472135955 + -4 Combine like terms: 4 + -4 = 0 0 + w = -4.472135955 + -4 w = -4.472135955 + -4 Combine like terms: -4.472135955 + -4 = -8.472135955 w = -8.472135955 Simplifying w = -8.472135955

Solution

The solution to the problem is based on the solutions from the subproblems. w = {0.472135955, -8.472135955}

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