-16x^2+40x-5=0

Solution for -16x^2+40x-5=0 equation:

Simplifying
-16x2 + 40x + -5 = 0

Reorder the terms:
-5 + 40x + -16x2 = 0

Solving
-5 + 40x + -16x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-16 the coefficient of the squared term: 

Divide each side by '-16'.
0.3125 + -2.5x + x2 = 0

Move the constant term to the right:

Add '-0.3125' to each side of the equation.
0.3125 + -2.5x + -0.3125 + x2 = 0 + -0.3125

Reorder the terms:
0.3125 + -0.3125 + -2.5x + x2 = 0 + -0.3125

Combine like terms: 0.3125 + -0.3125 = 0.0000
0.0000 + -2.5x + x2 = 0 + -0.3125
-2.5x + x2 = 0 + -0.3125

Combine like terms: 0 + -0.3125 = -0.3125
-2.5x + x2 = -0.3125

The x term is -2.5x.  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.
-2.5x + 1.5625 + x2 = -0.3125 + 1.5625

Reorder the terms:
1.5625 + -2.5x + x2 = -0.3125 + 1.5625

Combine like terms: -0.3125 + 1.5625 = 1.25
1.5625 + -2.5x + x2 = 1.25

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

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(x + -1.25) equal to 1.118033989 and -1.118033989.

Subproblem 1
x + -1.25 = 1.118033989

Simplifying
x + -1.25 = 1.118033989

Reorder the terms:
-1.25 + x = 1.118033989

Solving
-1.25 + x = 1.118033989

Solving for variable 'x'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + x = 1.118033989 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + x = 1.118033989 + 1.25
x = 1.118033989 + 1.25

Combine like terms: 1.118033989 + 1.25 = 2.368033989
x = 2.368033989

Simplifying
x = 2.368033989

Subproblem 2
x + -1.25 = -1.118033989

Simplifying
x + -1.25 = -1.118033989

Reorder the terms:
-1.25 + x = -1.118033989

Solving
-1.25 + x = -1.118033989

Solving for variable 'x'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + x = -1.118033989 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + x = -1.118033989 + 1.25
x = -1.118033989 + 1.25

Combine like terms: -1.118033989 + 1.25 = 0.131966011
x = 0.131966011

Simplifying
x = 0.131966011

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.368033989, 0.131966011}