0=w^2+9w+16

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Solution for 0=w^2+9w+16 equation: 


Simplifying
0 = w2 + 9w + 16

Reorder the terms:
0 = 16 + 9w + w2

Solving
0 = 16 + 9w + w2

Solving for variable 'w'.

Combine like terms: 0 + -16 = -16
-16 + -9w + -1w2 = 16 + 9w + w2 + -16 + -9w + -1w2

Reorder the terms:
-16 + -9w + -1w2 = 16 + -16 + 9w + -9w + w2 + -1w2

Combine like terms: 16 + -16 = 0
-16 + -9w + -1w2 = 0 + 9w + -9w + w2 + -1w2
-16 + -9w + -1w2 = 9w + -9w + w2 + -1w2

Combine like terms: 9w + -9w = 0
-16 + -9w + -1w2 = 0 + w2 + -1w2
-16 + -9w + -1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
-16 + -9w + -1w2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(16 + 9w + w2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(16 + 9w + w2)' equal to zero and attempt to solve:

Simplifying
16 + 9w + w2 = 0

Solving
16 + 9w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-16' to each side of the equation.
16 + 9w + -16 + w2 = 0 + -16

Reorder the terms:
16 + -16 + 9w + w2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + 9w + w2 = 0 + -16
9w + w2 = 0 + -16

Combine like terms: 0 + -16 = -16
9w + w2 = -16

The w term is 9w.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9w + 20.25 + w2 = -16 + 20.25

Reorder the terms:
20.25 + 9w + w2 = -16 + 20.25

Combine like terms: -16 + 20.25 = 4.25
20.25 + 9w + w2 = 4.25

Factor a perfect square on the left side:
(w + 4.5)(w + 4.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(w + 4.5) equal to 2.061552813 and -2.061552813.


Subproblem 1
w + 4.5 = 2.061552813

Simplifying
w + 4.5 = 2.061552813

Reorder the terms:
4.5 + w = 2.061552813

Solving
4.5 + w = 2.061552813

Solving for variable 'w'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + w = 2.061552813 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + w = 2.061552813 + -4.5
w = 2.061552813 + -4.5

Combine like terms: 2.061552813 + -4.5 = -2.438447187
w = -2.438447187

Simplifying
w = -2.438447187


Subproblem 2
w + 4.5 = -2.061552813

Simplifying
w + 4.5 = -2.061552813

Reorder the terms:
4.5 + w = -2.061552813

Solving
4.5 + w = -2.061552813

Solving for variable 'w'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + w = -2.061552813 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + w = -2.061552813 + -4.5
w = -2.061552813 + -4.5

Combine like terms: -2.061552813 + -4.5 = -6.561552813
w = -6.561552813

Simplifying
w = -6.561552813


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {-2.438447187, -6.561552813}
Solution
w = {-2.438447187, -6.561552813}

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