w^2+9w+15=0

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Solution for w^2+9w+15=0 equation: 


Simplifying
w2 + 9w + 15 = 0

Reorder the terms:
15 + 9w + w2 = 0

Solving
15 + 9w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '-15' to each side of the equation.
15 + 9w + -15 + w2 = 0 + -15

Reorder the terms:
15 + -15 + 9w + w2 = 0 + -15

Combine like terms: 15 + -15 = 0
0 + 9w + w2 = 0 + -15
9w + w2 = 0 + -15

Combine like terms: 0 + -15 = -15
9w + w2 = -15

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 = -15 + 20.25

Reorder the terms:
20.25 + 9w + w2 = -15 + 20.25

Combine like terms: -15 + 20.25 = 5.25
20.25 + 9w + w2 = 5.25

Factor a perfect square on the left side:
(w + 4.5)(w + 4.5) = 5.25

Calculate the square root of the right side: 2.291287847

Break this problem into two subproblems by setting 
(w + 4.5) equal to 2.291287847 and -2.291287847.


Subproblem 1
w + 4.5 = 2.291287847

Simplifying
w + 4.5 = 2.291287847

Reorder the terms:
4.5 + w = 2.291287847

Solving
4.5 + w = 2.291287847

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 = 2.291287847 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + w = 2.291287847 + -4.5
w = 2.291287847 + -4.5

Combine like terms: 2.291287847 + -4.5 = -2.208712153
w = -2.208712153

Simplifying
w = -2.208712153


Subproblem 2
w + 4.5 = -2.291287847

Simplifying
w + 4.5 = -2.291287847

Reorder the terms:
4.5 + w = -2.291287847

Solving
4.5 + w = -2.291287847

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 = -2.291287847 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + w = -2.291287847 + -4.5
w = -2.291287847 + -4.5

Combine like terms: -2.291287847 + -4.5 = -6.791287847
w = -6.791287847

Simplifying
w = -6.791287847


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {-2.208712153, -6.791287847}

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