0=w^2+5w-88

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Solution for 0=w^2+5w-88 equation:


Simplifying
0 = w2 + 5w + -88

Reorder the terms:
0 = -88 + 5w + w2

Solving
0 = -88 + 5w + w2

Solving for variable 'w'.

Combine like terms: 0 + 88 = 88
88 + -5w + -1w2 = -88 + 5w + w2 + 88 + -5w + -1w2

Reorder the terms:
88 + -5w + -1w2 = -88 + 88 + 5w + -5w + w2 + -1w2

Combine like terms: -88 + 88 = 0
88 + -5w + -1w2 = 0 + 5w + -5w + w2 + -1w2
88 + -5w + -1w2 = 5w + -5w + w2 + -1w2

Combine like terms: 5w + -5w = 0
88 + -5w + -1w2 = 0 + w2 + -1w2
88 + -5w + -1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
88 + -5w + -1w2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-88 + 5w + w2 = 0

Move the constant term to the right:

Add '88' to each side of the equation.
-88 + 5w + 88 + w2 = 0 + 88

Reorder the terms:
-88 + 88 + 5w + w2 = 0 + 88

Combine like terms: -88 + 88 = 0
0 + 5w + w2 = 0 + 88
5w + w2 = 0 + 88

Combine like terms: 0 + 88 = 88
5w + w2 = 88

The w term is 5w.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5w + 6.25 + w2 = 88 + 6.25

Reorder the terms:
6.25 + 5w + w2 = 88 + 6.25

Combine like terms: 88 + 6.25 = 94.25
6.25 + 5w + w2 = 94.25

Factor a perfect square on the left side:
(w + 2.5)(w + 2.5) = 94.25

Calculate the square root of the right side: 9.708243919

Break this problem into two subproblems by setting 
(w + 2.5) equal to 9.708243919 and -9.708243919.

Subproblem 1

w + 2.5 = 9.708243919 Simplifying w + 2.5 = 9.708243919 Reorder the terms: 2.5 + w = 9.708243919 Solving 2.5 + w = 9.708243919 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + w = 9.708243919 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + w = 9.708243919 + -2.5 w = 9.708243919 + -2.5 Combine like terms: 9.708243919 + -2.5 = 7.208243919 w = 7.208243919 Simplifying w = 7.208243919

Subproblem 2

w + 2.5 = -9.708243919 Simplifying w + 2.5 = -9.708243919 Reorder the terms: 2.5 + w = -9.708243919 Solving 2.5 + w = -9.708243919 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + w = -9.708243919 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + w = -9.708243919 + -2.5 w = -9.708243919 + -2.5 Combine like terms: -9.708243919 + -2.5 = -12.208243919 w = -12.208243919 Simplifying w = -12.208243919

Solution

The solution to the problem is based on the solutions from the subproblems. w = {7.208243919, -12.208243919}

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