w^2+17w-4=0

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Solution for w^2+17w-4=0 equation: 


Simplifying
w2 + 17w + -4 = 0

Reorder the terms:
-4 + 17w + w2 = 0

Solving
-4 + 17w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 17w + 4 + w2 = 0 + 4

Reorder the terms:
-4 + 4 + 17w + w2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 17w + w2 = 0 + 4
17w + w2 = 0 + 4

Combine like terms: 0 + 4 = 4
17w + w2 = 4

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 = 4 + 72.25

Reorder the terms:
72.25 + 17w + w2 = 4 + 72.25

Combine like terms: 4 + 72.25 = 76.25
72.25 + 17w + w2 = 76.25

Factor a perfect square on the left side:
(w + 8.5)(w + 8.5) = 76.25

Calculate the square root of the right side: 8.732124598

Break this problem into two subproblems by setting 
(w + 8.5) equal to 8.732124598 and -8.732124598.


Subproblem 1
w + 8.5 = 8.732124598

Simplifying
w + 8.5 = 8.732124598

Reorder the terms:
8.5 + w = 8.732124598

Solving
8.5 + w = 8.732124598

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 = 8.732124598 + -8.5

Combine like terms: 8.5 + -8.5 = 0.0
0.0 + w = 8.732124598 + -8.5
w = 8.732124598 + -8.5

Combine like terms: 8.732124598 + -8.5 = 0.232124598
w = 0.232124598

Simplifying
w = 0.232124598


Subproblem 2
w + 8.5 = -8.732124598

Simplifying
w + 8.5 = -8.732124598

Reorder the terms:
8.5 + w = -8.732124598

Solving
8.5 + w = -8.732124598

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 = -8.732124598 + -8.5

Combine like terms: 8.5 + -8.5 = 0.0
0.0 + w = -8.732124598 + -8.5
w = -8.732124598 + -8.5

Combine like terms: -8.732124598 + -8.5 = -17.232124598
w = -17.232124598

Simplifying
w = -17.232124598


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {0.232124598, -17.232124598}

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