2(2w+5)(w)=250

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Solution for 2(2w+5)(w)=250 equation: 


Simplifying
2(2w + 5)(w) = 250

Reorder the terms:
2(5 + 2w)(w) = 250

Reorder the terms for easier multiplication:
2w(5 + 2w) = 250
(5 * 2w + 2w * 2w) = 250
(10w + 4w2) = 250

Solving
10w + 4w2 = 250

Solving for variable 'w'.

Reorder the terms:
-250 + 10w + 4w2 = 250 + -250

Combine like terms: 250 + -250 = 0
-250 + 10w + 4w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-125 + 5w + 2w2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-125 + 5w + 2w2)' equal to zero and attempt to solve:

Simplifying
-125 + 5w + 2w2 = 0

Solving
-125 + 5w + 2w2 = 0

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

Divide each side by '2'.
-62.5 + 2.5w + w2 = 0

Move the constant term to the right:

Add '62.5' to each side of the equation.
-62.5 + 2.5w + 62.5 + w2 = 0 + 62.5

Reorder the terms:
-62.5 + 62.5 + 2.5w + w2 = 0 + 62.5

Combine like terms: -62.5 + 62.5 = 0.0
0.0 + 2.5w + w2 = 0 + 62.5
2.5w + w2 = 0 + 62.5

Combine like terms: 0 + 62.5 = 62.5
2.5w + w2 = 62.5

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 = 62.5 + 1.5625

Reorder the terms:
1.5625 + 2.5w + w2 = 62.5 + 1.5625

Combine like terms: 62.5 + 1.5625 = 64.0625
1.5625 + 2.5w + w2 = 64.0625

Factor a perfect square on the left side:
(w + 1.25)(w + 1.25) = 64.0625

Calculate the square root of the right side: 8.003905297

Break this problem into two subproblems by setting 
(w + 1.25) equal to 8.003905297 and -8.003905297.


Subproblem 1
w + 1.25 = 8.003905297

Simplifying
w + 1.25 = 8.003905297

Reorder the terms:
1.25 + w = 8.003905297

Solving
1.25 + w = 8.003905297

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 = 8.003905297 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + w = 8.003905297 + -1.25
w = 8.003905297 + -1.25

Combine like terms: 8.003905297 + -1.25 = 6.753905297
w = 6.753905297

Simplifying
w = 6.753905297


Subproblem 2
w + 1.25 = -8.003905297

Simplifying
w + 1.25 = -8.003905297

Reorder the terms:
1.25 + w = -8.003905297

Solving
1.25 + w = -8.003905297

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 = -8.003905297 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + w = -8.003905297 + -1.25
w = -8.003905297 + -1.25

Combine like terms: -8.003905297 + -1.25 = -9.253905297
w = -9.253905297

Simplifying
w = -9.253905297


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {6.753905297, -9.253905297}
Solution
w = {6.753905297, -9.253905297}

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