10w^2-36w+16=0

Solution for 10w^2-36w+16=0 equation:

Simplifying
10w2 + -36w + 16 = 0

Reorder the terms:
16 + -36w + 10w2 = 0

Solving
16 + -36w + 10w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2'.
2(8 + -18w + 5w2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(8 + -18w + 5w2)' equal to zero and attempt to solve:

Simplifying
8 + -18w + 5w2 = 0

Solving
8 + -18w + 5w2 = 0

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

Divide each side by '5'.
1.6 + -3.6w + w2 = 0

Move the constant term to the right:

Add '-1.6' to each side of the equation.
1.6 + -3.6w + -1.6 + w2 = 0 + -1.6

Reorder the terms:
1.6 + -1.6 + -3.6w + w2 = 0 + -1.6

Combine like terms: 1.6 + -1.6 = 0.0
0.0 + -3.6w + w2 = 0 + -1.6
-3.6w + w2 = 0 + -1.6

Combine like terms: 0 + -1.6 = -1.6
-3.6w + w2 = -1.6

The w term is -3.6w.  Take half its coefficient (-1.8).
Square it (3.24) and add it to both sides.

Add '3.24' to each side of the equation.
-3.6w + 3.24 + w2 = -1.6 + 3.24

Reorder the terms:
3.24 + -3.6w + w2 = -1.6 + 3.24

Combine like terms: -1.6 + 3.24 = 1.64
3.24 + -3.6w + w2 = 1.64

Factor a perfect square on the left side:
(w + -1.8)(w + -1.8) = 1.64

Calculate the square root of the right side: 1.280624847

Break this problem into two subproblems by setting 
(w + -1.8) equal to 1.280624847 and -1.280624847.

Subproblem 1
w + -1.8 = 1.280624847

Simplifying
w + -1.8 = 1.280624847

Reorder the terms:
-1.8 + w = 1.280624847

Solving
-1.8 + w = 1.280624847

Solving for variable 'w'.

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

Add '1.8' to each side of the equation.
-1.8 + 1.8 + w = 1.280624847 + 1.8

Combine like terms: -1.8 + 1.8 = 0.0
0.0 + w = 1.280624847 + 1.8
w = 1.280624847 + 1.8

Combine like terms: 1.280624847 + 1.8 = 3.080624847
w = 3.080624847

Simplifying
w = 3.080624847

Subproblem 2
w + -1.8 = -1.280624847

Simplifying
w + -1.8 = -1.280624847

Reorder the terms:
-1.8 + w = -1.280624847

Solving
-1.8 + w = -1.280624847

Solving for variable 'w'.

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

Add '1.8' to each side of the equation.
-1.8 + 1.8 + w = -1.280624847 + 1.8

Combine like terms: -1.8 + 1.8 = 0.0
0.0 + w = -1.280624847 + 1.8
w = -1.280624847 + 1.8

Combine like terms: -1.280624847 + 1.8 = 0.519375153
w = 0.519375153

Simplifying
w = 0.519375153

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {3.080624847, 0.519375153}
Solution
w = {3.080624847, 0.519375153}