63-2w^2+4w=0

Solution for 63-2w^2+4w=0 equation:

Simplifying
63 + -2w2 + 4w = 0

Reorder the terms:
63 + 4w + -2w2 = 0

Solving
63 + 4w + -2w2 = 0

Solving for variable 'w'.

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-31.5 + -2w + w2 = 0

Move the constant term to the right:

Add '31.5' to each side of the equation.
-31.5 + -2w + 31.5 + w2 = 0 + 31.5

Reorder the terms:
-31.5 + 31.5 + -2w + w2 = 0 + 31.5

Combine like terms: -31.5 + 31.5 = 0.0
0.0 + -2w + w2 = 0 + 31.5
-2w + w2 = 0 + 31.5

Combine like terms: 0 + 31.5 = 31.5
-2w + w2 = 31.5

The w term is -2w.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2w + 1 + w2 = 31.5 + 1

Reorder the terms:
1 + -2w + w2 = 31.5 + 1

Combine like terms: 31.5 + 1 = 32.5
1 + -2w + w2 = 32.5

Factor a perfect square on the left side:
(w + -1)(w + -1) = 32.5

Calculate the square root of the right side: 5.700877125

Break this problem into two subproblems by setting 
(w + -1) equal to 5.700877125 and -5.700877125.

Subproblem 1
w + -1 = 5.700877125

Simplifying
w + -1 = 5.700877125

Reorder the terms:
-1 + w = 5.700877125

Solving
-1 + w = 5.700877125

Solving for variable 'w'.

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

Add '1' to each side of the equation.
-1 + 1 + w = 5.700877125 + 1

Combine like terms: -1 + 1 = 0
0 + w = 5.700877125 + 1
w = 5.700877125 + 1

Combine like terms: 5.700877125 + 1 = 6.700877125
w = 6.700877125

Simplifying
w = 6.700877125

Subproblem 2
w + -1 = -5.700877125

Simplifying
w + -1 = -5.700877125

Reorder the terms:
-1 + w = -5.700877125

Solving
-1 + w = -5.700877125

Solving for variable 'w'.

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

Add '1' to each side of the equation.
-1 + 1 + w = -5.700877125 + 1

Combine like terms: -1 + 1 = 0
0 + w = -5.700877125 + 1
w = -5.700877125 + 1

Combine like terms: -5.700877125 + 1 = -4.700877125
w = -4.700877125

Simplifying
w = -4.700877125

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {6.700877125, -4.700877125}