2w^2+15w-100=0

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Solution for 2w^2+15w-100=0 equation:


Simplifying
2w2 + 15w + -100 = 0

Reorder the terms:
-100 + 15w + 2w2 = 0

Solving
-100 + 15w + 2w2 = 0

Solving for variable 'w'.

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

Divide each side by '2'.
-50 + 7.5w + w2 = 0

Move the constant term to the right:

Add '50' to each side of the equation.
-50 + 7.5w + 50 + w2 = 0 + 50

Reorder the terms:
-50 + 50 + 7.5w + w2 = 0 + 50

Combine like terms: -50 + 50 = 0
0 + 7.5w + w2 = 0 + 50
7.5w + w2 = 0 + 50

Combine like terms: 0 + 50 = 50
7.5w + w2 = 50

The w term is 7.5w.  Take half its coefficient (3.75).
Square it (14.0625) and add it to both sides.

Add '14.0625' to each side of the equation.
7.5w + 14.0625 + w2 = 50 + 14.0625

Reorder the terms:
14.0625 + 7.5w + w2 = 50 + 14.0625

Combine like terms: 50 + 14.0625 = 64.0625
14.0625 + 7.5w + w2 = 64.0625

Factor a perfect square on the left side:
(w + 3.75)(w + 3.75) = 64.0625

Calculate the square root of the right side: 8.003905297

Break this problem into two subproblems by setting 
(w + 3.75) equal to 8.003905297 and -8.003905297.

Subproblem 1

w + 3.75 = 8.003905297 Simplifying w + 3.75 = 8.003905297 Reorder the terms: 3.75 + w = 8.003905297 Solving 3.75 + w = 8.003905297 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + w = 8.003905297 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + w = 8.003905297 + -3.75 w = 8.003905297 + -3.75 Combine like terms: 8.003905297 + -3.75 = 4.253905297 w = 4.253905297 Simplifying w = 4.253905297

Subproblem 2

w + 3.75 = -8.003905297 Simplifying w + 3.75 = -8.003905297 Reorder the terms: 3.75 + w = -8.003905297 Solving 3.75 + w = -8.003905297 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + w = -8.003905297 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + w = -8.003905297 + -3.75 w = -8.003905297 + -3.75 Combine like terms: -8.003905297 + -3.75 = -11.753905297 w = -11.753905297 Simplifying w = -11.753905297

Solution

The solution to the problem is based on the solutions from the subproblems. w = {4.253905297, -11.753905297}

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