62=w(2w+8)

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Solution for 62=w(2w+8) equation: 


Simplifying
62 = w(2w + 8)

Reorder the terms:
62 = w(8 + 2w)
62 = (8 * w + 2w * w)
62 = (8w + 2w2)

Solving
62 = 8w + 2w2

Solving for variable 'w'.

Reorder the terms:
62 + -8w + -2w2 = 8w + -8w + 2w2 + -2w2

Combine like terms: 8w + -8w = 0
62 + -8w + -2w2 = 0 + 2w2 + -2w2
62 + -8w + -2w2 = 2w2 + -2w2

Combine like terms: 2w2 + -2w2 = 0
62 + -8w + -2w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(31 + -4w + -1w2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(31 + -4w + -1w2)' equal to zero and attempt to solve:

Simplifying
31 + -4w + -1w2 = 0

Solving
31 + -4w + -1w2 = 0

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

Divide each side by '-1'.
-31 + 4w + w2 = 0

Move the constant term to the right:

Add '31' to each side of the equation.
-31 + 4w + 31 + w2 = 0 + 31

Reorder the terms:
-31 + 31 + 4w + w2 = 0 + 31

Combine like terms: -31 + 31 = 0
0 + 4w + w2 = 0 + 31
4w + w2 = 0 + 31

Combine like terms: 0 + 31 = 31
4w + w2 = 31

The w term is 4w.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4w + 4 + w2 = 31 + 4

Reorder the terms:
4 + 4w + w2 = 31 + 4

Combine like terms: 31 + 4 = 35
4 + 4w + w2 = 35

Factor a perfect square on the left side:
(w + 2)(w + 2) = 35

Calculate the square root of the right side: 5.916079783

Break this problem into two subproblems by setting 
(w + 2) equal to 5.916079783 and -5.916079783.


Subproblem 1
w + 2 = 5.916079783

Simplifying
w + 2 = 5.916079783

Reorder the terms:
2 + w = 5.916079783

Solving
2 + w = 5.916079783

Solving for variable 'w'.

Move all terms containing w to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + w = 5.916079783 + -2

Combine like terms: 2 + -2 = 0
0 + w = 5.916079783 + -2
w = 5.916079783 + -2

Combine like terms: 5.916079783 + -2 = 3.916079783
w = 3.916079783

Simplifying
w = 3.916079783


Subproblem 2
w + 2 = -5.916079783

Simplifying
w + 2 = -5.916079783

Reorder the terms:
2 + w = -5.916079783

Solving
2 + w = -5.916079783

Solving for variable 'w'.

Move all terms containing w to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + w = -5.916079783 + -2

Combine like terms: 2 + -2 = 0
0 + w = -5.916079783 + -2
w = -5.916079783 + -2

Combine like terms: -5.916079783 + -2 = -7.916079783
w = -7.916079783

Simplifying
w = -7.916079783


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {3.916079783, -7.916079783}
Solution
w = {3.916079783, -7.916079783}

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