-5w^2=-(17w-5)

Solution for -5w^2=-(17w-5) equation:

Simplifying
-5w2 = -1(17w + -5)

Reorder the terms:
-5w2 = -1(-5 + 17w)
-5w2 = (-5 * -1 + 17w * -1)
-5w2 = (5 + -17w)

Solving
-5w2 = 5 + -17w

Solving for variable 'w'.

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

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

Combine like terms: 5 + -5 = 0
-5 + 17w + -5w2 = 0 + -17w + 17w
-5 + 17w + -5w2 = -17w + 17w

Combine like terms: -17w + 17w = 0
-5 + 17w + -5w2 = 0

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

Divide each side by '-5'.
1 + -3.4w + w2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -3.4w + -1 + w2 = 0 + -1

Reorder the terms:
1 + -1 + -3.4w + w2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3.4w + w2 = 0 + -1
-3.4w + w2 = 0 + -1

Combine like terms: 0 + -1 = -1
-3.4w + w2 = -1

The w term is -3.4w.  Take half its coefficient (-1.7).
Square it (2.89) and add it to both sides.

Add '2.89' to each side of the equation.
-3.4w + 2.89 + w2 = -1 + 2.89

Reorder the terms:
2.89 + -3.4w + w2 = -1 + 2.89

Combine like terms: -1 + 2.89 = 1.89
2.89 + -3.4w + w2 = 1.89

Factor a perfect square on the left side:
(w + -1.7)(w + -1.7) = 1.89

Calculate the square root of the right side: 1.374772708

Break this problem into two subproblems by setting 
(w + -1.7) equal to 1.374772708 and -1.374772708.

Subproblem 1
w + -1.7 = 1.374772708

Simplifying
w + -1.7 = 1.374772708

Reorder the terms:
-1.7 + w = 1.374772708

Solving
-1.7 + w = 1.374772708

Solving for variable 'w'.

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

Add '1.7' to each side of the equation.
-1.7 + 1.7 + w = 1.374772708 + 1.7

Combine like terms: -1.7 + 1.7 = 0.0
0.0 + w = 1.374772708 + 1.7
w = 1.374772708 + 1.7

Combine like terms: 1.374772708 + 1.7 = 3.074772708
w = 3.074772708

Simplifying
w = 3.074772708

Subproblem 2
w + -1.7 = -1.374772708

Simplifying
w + -1.7 = -1.374772708

Reorder the terms:
-1.7 + w = -1.374772708

Solving
-1.7 + w = -1.374772708

Solving for variable 'w'.

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

Add '1.7' to each side of the equation.
-1.7 + 1.7 + w = -1.374772708 + 1.7

Combine like terms: -1.7 + 1.7 = 0.0
0.0 + w = -1.374772708 + 1.7
w = -1.374772708 + 1.7

Combine like terms: -1.374772708 + 1.7 = 0.325227292
w = 0.325227292

Simplifying
w = 0.325227292

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {3.074772708, 0.325227292}