4w^2-10w-40=0

Solution for 4w^2-10w-40=0 equation:

Simplifying
4w2 + -10w + -40 = 0

Reorder the terms:
-40 + -10w + 4w2 = 0

Solving
-40 + -10w + 4w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-20 + -5w + 2w2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-20 + -5w + 2w2)' equal to zero and attempt to solve:

Simplifying
-20 + -5w + 2w2 = 0

Solving
-20 + -5w + 2w2 = 0

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

Divide each side by '2'.
-10 + -2.5w + w2 = 0

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + -2.5w + 10 + w2 = 0 + 10

Reorder the terms:
-10 + 10 + -2.5w + w2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -2.5w + w2 = 0 + 10
-2.5w + w2 = 0 + 10

Combine like terms: 0 + 10 = 10
-2.5w + w2 = 10

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 = 10 + 1.5625

Reorder the terms:
1.5625 + -2.5w + w2 = 10 + 1.5625

Combine like terms: 10 + 1.5625 = 11.5625
1.5625 + -2.5w + w2 = 11.5625

Factor a perfect square on the left side:
(w + -1.25)(w + -1.25) = 11.5625

Calculate the square root of the right side: 3.400367627

Break this problem into two subproblems by setting 
(w + -1.25) equal to 3.400367627 and -3.400367627.

Subproblem 1
w + -1.25 = 3.400367627

Simplifying
w + -1.25 = 3.400367627

Reorder the terms:
-1.25 + w = 3.400367627

Solving
-1.25 + w = 3.400367627

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 = 3.400367627 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + w = 3.400367627 + 1.25
w = 3.400367627 + 1.25

Combine like terms: 3.400367627 + 1.25 = 4.650367627
w = 4.650367627

Simplifying
w = 4.650367627

Subproblem 2
w + -1.25 = -3.400367627

Simplifying
w + -1.25 = -3.400367627

Reorder the terms:
-1.25 + w = -3.400367627

Solving
-1.25 + w = -3.400367627

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 = -3.400367627 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + w = -3.400367627 + 1.25
w = -3.400367627 + 1.25

Combine like terms: -3.400367627 + 1.25 = -2.150367627
w = -2.150367627

Simplifying
w = -2.150367627

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {4.650367627, -2.150367627}
Solution
w = {4.650367627, -2.150367627}