-5w^2-6w+17=8

Solution for -5w^2-6w+17=8 equation:

Simplifying
-5w2 + -6w + 17 = 8

Reorder the terms:
17 + -6w + -5w2 = 8

Solving
17 + -6w + -5w2 = 8

Solving for variable 'w'.

Reorder the terms:
17 + -8 + -6w + -5w2 = 8 + -8

Combine like terms: 17 + -8 = 9
9 + -6w + -5w2 = 8 + -8

Combine like terms: 8 + -8 = 0
9 + -6w + -5w2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-1.8 + 1.2w + w2 = 0

Move the constant term to the right:

Add '1.8' to each side of the equation.
-1.8 + 1.2w + 1.8 + w2 = 0 + 1.8

Reorder the terms:
-1.8 + 1.8 + 1.2w + w2 = 0 + 1.8

Combine like terms: -1.8 + 1.8 = 0.0
0.0 + 1.2w + w2 = 0 + 1.8
1.2w + w2 = 0 + 1.8

Combine like terms: 0 + 1.8 = 1.8
1.2w + w2 = 1.8

The w term is 1.2w.  Take half its coefficient (0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
1.2w + 0.36 + w2 = 1.8 + 0.36

Reorder the terms:
0.36 + 1.2w + w2 = 1.8 + 0.36

Combine like terms: 1.8 + 0.36 = 2.16
0.36 + 1.2w + w2 = 2.16

Factor a perfect square on the left side:
(w + 0.6)(w + 0.6) = 2.16

Calculate the square root of the right side: 1.469693846

Break this problem into two subproblems by setting 
(w + 0.6) equal to 1.469693846 and -1.469693846.

Subproblem 1
w + 0.6 = 1.469693846

Simplifying
w + 0.6 = 1.469693846

Reorder the terms:
0.6 + w = 1.469693846

Solving
0.6 + w = 1.469693846

Solving for variable 'w'.

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

Add '-0.6' to each side of the equation.
0.6 + -0.6 + w = 1.469693846 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + w = 1.469693846 + -0.6
w = 1.469693846 + -0.6

Combine like terms: 1.469693846 + -0.6 = 0.869693846
w = 0.869693846

Simplifying
w = 0.869693846

Subproblem 2
w + 0.6 = -1.469693846

Simplifying
w + 0.6 = -1.469693846

Reorder the terms:
0.6 + w = -1.469693846

Solving
0.6 + w = -1.469693846

Solving for variable 'w'.

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

Add '-0.6' to each side of the equation.
0.6 + -0.6 + w = -1.469693846 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + w = -1.469693846 + -0.6
w = -1.469693846 + -0.6

Combine like terms: -1.469693846 + -0.6 = -2.069693846
w = -2.069693846

Simplifying
w = -2.069693846

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {0.869693846, -2.069693846}