W^2+16W+24=0

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Solution for W^2+16W+24=0 equation: 


Simplifying
W2 + 16W + 24 = 0

Reorder the terms:
24 + 16W + W2 = 0

Solving
24 + 16W + W2 = 0

Solving for variable 'W'.

Begin completing the square.

Move the constant term to the right:

Add '-24' to each side of the equation.
24 + 16W + -24 + W2 = 0 + -24

Reorder the terms:
24 + -24 + 16W + W2 = 0 + -24

Combine like terms: 24 + -24 = 0
0 + 16W + W2 = 0 + -24
16W + W2 = 0 + -24

Combine like terms: 0 + -24 = -24
16W + W2 = -24

The W term is 16W.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16W + 64 + W2 = -24 + 64

Reorder the terms:
64 + 16W + W2 = -24 + 64

Combine like terms: -24 + 64 = 40
64 + 16W + W2 = 40

Factor a perfect square on the left side:
(W + 8)(W + 8) = 40

Calculate the square root of the right side: 6.32455532

Break this problem into two subproblems by setting 
(W + 8) equal to 6.32455532 and -6.32455532.


Subproblem 1
W + 8 = 6.32455532

Simplifying
W + 8 = 6.32455532

Reorder the terms:
8 + W = 6.32455532

Solving
8 + W = 6.32455532

Solving for variable 'W'.

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

Add '-8' to each side of the equation.
8 + -8 + W = 6.32455532 + -8

Combine like terms: 8 + -8 = 0
0 + W = 6.32455532 + -8
W = 6.32455532 + -8

Combine like terms: 6.32455532 + -8 = -1.67544468
W = -1.67544468

Simplifying
W = -1.67544468


Subproblem 2
W + 8 = -6.32455532

Simplifying
W + 8 = -6.32455532

Reorder the terms:
8 + W = -6.32455532

Solving
8 + W = -6.32455532

Solving for variable 'W'.

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

Add '-8' to each side of the equation.
8 + -8 + W = -6.32455532 + -8

Combine like terms: 8 + -8 = 0
0 + W = -6.32455532 + -8
W = -6.32455532 + -8

Combine like terms: -6.32455532 + -8 = -14.32455532
W = -14.32455532

Simplifying
W = -14.32455532


Solution
The solution to the problem is based on the solutions
from the subproblems.
W = {-1.67544468, -14.32455532}

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