w^2+17w-28=0

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Solution for w^2+17w-28=0 equation: 


Simplifying
w2 + 17w + -28 = 0

Reorder the terms:
-28 + 17w + w2 = 0

Solving
-28 + 17w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '28' to each side of the equation.
-28 + 17w + 28 + w2 = 0 + 28

Reorder the terms:
-28 + 28 + 17w + w2 = 0 + 28

Combine like terms: -28 + 28 = 0
0 + 17w + w2 = 0 + 28
17w + w2 = 0 + 28

Combine like terms: 0 + 28 = 28
17w + w2 = 28

The w term is 17w.  Take half its coefficient (8.5).
Square it (72.25) and add it to both sides.

Add '72.25' to each side of the equation.
17w + 72.25 + w2 = 28 + 72.25

Reorder the terms:
72.25 + 17w + w2 = 28 + 72.25

Combine like terms: 28 + 72.25 = 100.25
72.25 + 17w + w2 = 100.25

Factor a perfect square on the left side:
(w + 8.5)(w + 8.5) = 100.25

Calculate the square root of the right side: 10.012492197

Break this problem into two subproblems by setting 
(w + 8.5) equal to 10.012492197 and -10.012492197.


Subproblem 1
w + 8.5 = 10.012492197

Simplifying
w + 8.5 = 10.012492197

Reorder the terms:
8.5 + w = 10.012492197

Solving
8.5 + w = 10.012492197

Solving for variable 'w'.

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

Add '-8.5' to each side of the equation.
8.5 + -8.5 + w = 10.012492197 + -8.5

Combine like terms: 8.5 + -8.5 = 0.0
0.0 + w = 10.012492197 + -8.5
w = 10.012492197 + -8.5

Combine like terms: 10.012492197 + -8.5 = 1.512492197
w = 1.512492197

Simplifying
w = 1.512492197


Subproblem 2
w + 8.5 = -10.012492197

Simplifying
w + 8.5 = -10.012492197

Reorder the terms:
8.5 + w = -10.012492197

Solving
8.5 + w = -10.012492197

Solving for variable 'w'.

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

Add '-8.5' to each side of the equation.
8.5 + -8.5 + w = -10.012492197 + -8.5

Combine like terms: 8.5 + -8.5 = 0.0
0.0 + w = -10.012492197 + -8.5
w = -10.012492197 + -8.5

Combine like terms: -10.012492197 + -8.5 = -18.512492197
w = -18.512492197

Simplifying
w = -18.512492197


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {1.512492197, -18.512492197}

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