2(2w+5)(w)=259

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Solution for 2(2w+5)(w)=259 equation:


Simplifying
2(2w + 5)(w) = 259

Reorder the terms:
2(5 + 2w)(w) = 259

Reorder the terms for easier multiplication:
2w(5 + 2w) = 259
(5 * 2w + 2w * 2w) = 259
(10w + 4w2) = 259

Solving
10w + 4w2 = 259

Solving for variable 'w'.

Reorder the terms:
-259 + 10w + 4w2 = 259 + -259

Combine like terms: 259 + -259 = 0
-259 + 10w + 4w2 = 0

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

Divide each side by '4'.
-64.75 + 2.5w + w2 = 0

Move the constant term to the right:

Add '64.75' to each side of the equation.
-64.75 + 2.5w + 64.75 + w2 = 0 + 64.75

Reorder the terms:
-64.75 + 64.75 + 2.5w + w2 = 0 + 64.75

Combine like terms: -64.75 + 64.75 = 0.00
0.00 + 2.5w + w2 = 0 + 64.75
2.5w + w2 = 0 + 64.75

Combine like terms: 0 + 64.75 = 64.75
2.5w + w2 = 64.75

The w term is 2.5w.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5w + 1.5625 + w2 = 64.75 + 1.5625

Reorder the terms:
1.5625 + 2.5w + w2 = 64.75 + 1.5625

Combine like terms: 64.75 + 1.5625 = 66.3125
1.5625 + 2.5w + w2 = 66.3125

Factor a perfect square on the left side:
(w + 1.25)(w + 1.25) = 66.3125

Calculate the square root of the right side: 8.143248737

Break this problem into two subproblems by setting 
(w + 1.25) equal to 8.143248737 and -8.143248737.

Subproblem 1

w + 1.25 = 8.143248737 Simplifying w + 1.25 = 8.143248737 Reorder the terms: 1.25 + w = 8.143248737 Solving 1.25 + w = 8.143248737 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + w = 8.143248737 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + w = 8.143248737 + -1.25 w = 8.143248737 + -1.25 Combine like terms: 8.143248737 + -1.25 = 6.893248737 w = 6.893248737 Simplifying w = 6.893248737

Subproblem 2

w + 1.25 = -8.143248737 Simplifying w + 1.25 = -8.143248737 Reorder the terms: 1.25 + w = -8.143248737 Solving 1.25 + w = -8.143248737 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + w = -8.143248737 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + w = -8.143248737 + -1.25 w = -8.143248737 + -1.25 Combine like terms: -8.143248737 + -1.25 = -9.393248737 w = -9.393248737 Simplifying w = -9.393248737

Solution

The solution to the problem is based on the solutions from the subproblems. w = {6.893248737, -9.393248737}

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