80=w(2w+10)

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Solution for 80=w(2w+10) equation: 


Simplifying
80 = w(2w + 10)

Reorder the terms:
80 = w(10 + 2w)
80 = (10 * w + 2w * w)
80 = (10w + 2w2)

Solving
80 = 10w + 2w2

Solving for variable 'w'.

Reorder the terms:
80 + -10w + -2w2 = 10w + -10w + 2w2 + -2w2

Combine like terms: 10w + -10w = 0
80 + -10w + -2w2 = 0 + 2w2 + -2w2
80 + -10w + -2w2 = 2w2 + -2w2

Combine like terms: 2w2 + -2w2 = 0
80 + -10w + -2w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(40 + -5w + -1w2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(40 + -5w + -1w2)' equal to zero and attempt to solve:

Simplifying
40 + -5w + -1w2 = 0

Solving
40 + -5w + -1w2 = 0

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

Divide each side by '-1'.
-40 + 5w + w2 = 0

Move the constant term to the right:

Add '40' to each side of the equation.
-40 + 5w + 40 + w2 = 0 + 40

Reorder the terms:
-40 + 40 + 5w + w2 = 0 + 40

Combine like terms: -40 + 40 = 0
0 + 5w + w2 = 0 + 40
5w + w2 = 0 + 40

Combine like terms: 0 + 40 = 40
5w + w2 = 40

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 = 40 + 6.25

Reorder the terms:
6.25 + 5w + w2 = 40 + 6.25

Combine like terms: 40 + 6.25 = 46.25
6.25 + 5w + w2 = 46.25

Factor a perfect square on the left side:
(w + 2.5)(w + 2.5) = 46.25

Calculate the square root of the right side: 6.800735254

Break this problem into two subproblems by setting 
(w + 2.5) equal to 6.800735254 and -6.800735254.


Subproblem 1
w + 2.5 = 6.800735254

Simplifying
w + 2.5 = 6.800735254

Reorder the terms:
2.5 + w = 6.800735254

Solving
2.5 + w = 6.800735254

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 = 6.800735254 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + w = 6.800735254 + -2.5
w = 6.800735254 + -2.5

Combine like terms: 6.800735254 + -2.5 = 4.300735254
w = 4.300735254

Simplifying
w = 4.300735254


Subproblem 2
w + 2.5 = -6.800735254

Simplifying
w + 2.5 = -6.800735254

Reorder the terms:
2.5 + w = -6.800735254

Solving
2.5 + w = -6.800735254

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 = -6.800735254 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + w = -6.800735254 + -2.5
w = -6.800735254 + -2.5

Combine like terms: -6.800735254 + -2.5 = -9.300735254
w = -9.300735254

Simplifying
w = -9.300735254


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {4.300735254, -9.300735254}
Solution
w = {4.300735254, -9.300735254}

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