w^2+4w-91=0

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Solution for w^2+4w-91=0 equation:


Simplifying
w2 + 4w + -91 = 0

Reorder the terms:
-91 + 4w + w2 = 0

Solving
-91 + 4w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '91' to each side of the equation.
-91 + 4w + 91 + w2 = 0 + 91

Reorder the terms:
-91 + 91 + 4w + w2 = 0 + 91

Combine like terms: -91 + 91 = 0
0 + 4w + w2 = 0 + 91
4w + w2 = 0 + 91

Combine like terms: 0 + 91 = 91
4w + w2 = 91

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 = 91 + 4

Reorder the terms:
4 + 4w + w2 = 91 + 4

Combine like terms: 91 + 4 = 95
4 + 4w + w2 = 95

Factor a perfect square on the left side:
(w + 2)(w + 2) = 95

Calculate the square root of the right side: 9.746794345

Break this problem into two subproblems by setting 
(w + 2) equal to 9.746794345 and -9.746794345.

Subproblem 1

w + 2 = 9.746794345 Simplifying w + 2 = 9.746794345 Reorder the terms: 2 + w = 9.746794345 Solving 2 + w = 9.746794345 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 = 9.746794345 + -2 Combine like terms: 2 + -2 = 0 0 + w = 9.746794345 + -2 w = 9.746794345 + -2 Combine like terms: 9.746794345 + -2 = 7.746794345 w = 7.746794345 Simplifying w = 7.746794345

Subproblem 2

w + 2 = -9.746794345 Simplifying w + 2 = -9.746794345 Reorder the terms: 2 + w = -9.746794345 Solving 2 + w = -9.746794345 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 = -9.746794345 + -2 Combine like terms: 2 + -2 = 0 0 + w = -9.746794345 + -2 w = -9.746794345 + -2 Combine like terms: -9.746794345 + -2 = -11.746794345 w = -11.746794345 Simplifying w = -11.746794345

Solution

The solution to the problem is based on the solutions from the subproblems. w = {7.746794345, -11.746794345}

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