w^2+20w+16=0

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Solution for w^2+20w+16=0 equation: 


Simplifying
w2 + 20w + 16 = 0

Reorder the terms:
16 + 20w + w2 = 0

Solving
16 + 20w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '-16' to each side of the equation.
16 + 20w + -16 + w2 = 0 + -16

Reorder the terms:
16 + -16 + 20w + w2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + 20w + w2 = 0 + -16
20w + w2 = 0 + -16

Combine like terms: 0 + -16 = -16
20w + w2 = -16

The w term is 20w.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20w + 100 + w2 = -16 + 100

Reorder the terms:
100 + 20w + w2 = -16 + 100

Combine like terms: -16 + 100 = 84
100 + 20w + w2 = 84

Factor a perfect square on the left side:
(w + 10)(w + 10) = 84

Calculate the square root of the right side: 9.16515139

Break this problem into two subproblems by setting 
(w + 10) equal to 9.16515139 and -9.16515139.


Subproblem 1
w + 10 = 9.16515139

Simplifying
w + 10 = 9.16515139

Reorder the terms:
10 + w = 9.16515139

Solving
10 + w = 9.16515139

Solving for variable 'w'.

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

Add '-10' to each side of the equation.
10 + -10 + w = 9.16515139 + -10

Combine like terms: 10 + -10 = 0
0 + w = 9.16515139 + -10
w = 9.16515139 + -10

Combine like terms: 9.16515139 + -10 = -0.83484861
w = -0.83484861

Simplifying
w = -0.83484861


Subproblem 2
w + 10 = -9.16515139

Simplifying
w + 10 = -9.16515139

Reorder the terms:
10 + w = -9.16515139

Solving
10 + w = -9.16515139

Solving for variable 'w'.

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

Add '-10' to each side of the equation.
10 + -10 + w = -9.16515139 + -10

Combine like terms: 10 + -10 = 0
0 + w = -9.16515139 + -10
w = -9.16515139 + -10

Combine like terms: -9.16515139 + -10 = -19.16515139
w = -19.16515139

Simplifying
w = -19.16515139


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {-0.83484861, -19.16515139}

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