-16x^2+37x-20=0

Solution for -16x^2+37x-20=0 equation:

Simplifying
-16x2 + 37x + -20 = 0

Reorder the terms:
-20 + 37x + -16x2 = 0

Solving
-20 + 37x + -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'.
1.25 + -2.3125x + x2 = 0

Move the constant term to the right:

Add '-1.25' to each side of the equation.
1.25 + -2.3125x + -1.25 + x2 = 0 + -1.25

Reorder the terms:
1.25 + -1.25 + -2.3125x + x2 = 0 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + -2.3125x + x2 = 0 + -1.25
-2.3125x + x2 = 0 + -1.25

Combine like terms: 0 + -1.25 = -1.25
-2.3125x + x2 = -1.25

The x term is -2.3125x.  Take half its coefficient (-1.15625).
Square it (1.336914063) and add it to both sides.

Add '1.336914063' to each side of the equation.
-2.3125x + 1.336914063 + x2 = -1.25 + 1.336914063

Reorder the terms:
1.336914063 + -2.3125x + x2 = -1.25 + 1.336914063

Combine like terms: -1.25 + 1.336914063 = 0.086914063
1.336914063 + -2.3125x + x2 = 0.086914063

Factor a perfect square on the left side:
(x + -1.15625)(x + -1.15625) = 0.086914063

Calculate the square root of the right side: 0.294811911

Break this problem into two subproblems by setting 
(x + -1.15625) equal to 0.294811911 and -0.294811911.

Subproblem 1
x + -1.15625 = 0.294811911

Simplifying
x + -1.15625 = 0.294811911

Reorder the terms:
-1.15625 + x = 0.294811911

Solving
-1.15625 + x = 0.294811911

Solving for variable 'x'.

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

Add '1.15625' to each side of the equation.
-1.15625 + 1.15625 + x = 0.294811911 + 1.15625

Combine like terms: -1.15625 + 1.15625 = 0.00000
0.00000 + x = 0.294811911 + 1.15625
x = 0.294811911 + 1.15625

Combine like terms: 0.294811911 + 1.15625 = 1.451061911
x = 1.451061911

Simplifying
x = 1.451061911

Subproblem 2
x + -1.15625 = -0.294811911

Simplifying
x + -1.15625 = -0.294811911

Reorder the terms:
-1.15625 + x = -0.294811911

Solving
-1.15625 + x = -0.294811911

Solving for variable 'x'.

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

Add '1.15625' to each side of the equation.
-1.15625 + 1.15625 + x = -0.294811911 + 1.15625

Combine like terms: -1.15625 + 1.15625 = 0.00000
0.00000 + x = -0.294811911 + 1.15625
x = -0.294811911 + 1.15625

Combine like terms: -0.294811911 + 1.15625 = 0.861438089
x = 0.861438089

Simplifying
x = 0.861438089

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.451061911, 0.861438089}