-4w^2-10w+5=0

Solution for -4w^2-10w+5=0 equation:

Simplifying
-4w2 + -10w + 5 = 0

Reorder the terms:
5 + -10w + -4w2 = 0

Solving
5 + -10w + -4w2 = 0

Solving for variable 'w'.

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-1.25 + 2.5w + w2 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + 2.5w + 1.25 + w2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + 2.5w + w2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + 2.5w + w2 = 0 + 1.25
2.5w + w2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
2.5w + w2 = 1.25

The w term is 2.5w.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5w + 1.5625 + w2 = 1.25 + 1.5625

Reorder the terms:
1.5625 + 2.5w + w2 = 1.25 + 1.5625

Combine like terms: 1.25 + 1.5625 = 2.8125
1.5625 + 2.5w + w2 = 2.8125

Factor a perfect square on the left side:
(w + 1.25)(w + 1.25) = 2.8125

Calculate the square root of the right side: 1.677050983

Break this problem into two subproblems by setting 
(w + 1.25) equal to 1.677050983 and -1.677050983.

Subproblem 1
w + 1.25 = 1.677050983

Simplifying
w + 1.25 = 1.677050983

Reorder the terms:
1.25 + w = 1.677050983

Solving
1.25 + w = 1.677050983

Solving for variable 'w'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + w = 1.677050983 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + w = 1.677050983 + -1.25
w = 1.677050983 + -1.25

Combine like terms: 1.677050983 + -1.25 = 0.427050983
w = 0.427050983

Simplifying
w = 0.427050983

Subproblem 2
w + 1.25 = -1.677050983

Simplifying
w + 1.25 = -1.677050983

Reorder the terms:
1.25 + w = -1.677050983

Solving
1.25 + w = -1.677050983

Solving for variable 'w'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + w = -1.677050983 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + w = -1.677050983 + -1.25
w = -1.677050983 + -1.25

Combine like terms: -1.677050983 + -1.25 = -2.927050983
w = -2.927050983

Simplifying
w = -2.927050983

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {0.427050983, -2.927050983}