-16x^2+37x+6=0

Solution for -16x^2+37x+6=0 equation:

Simplifying
-16x2 + 37x + 6 = 0

Reorder the terms:
6 + 37x + -16x2 = 0

Solving
6 + 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'.
-0.375 + -2.3125x + x2 = 0

Move the constant term to the right:

Add '0.375' to each side of the equation.
-0.375 + -2.3125x + 0.375 + x2 = 0 + 0.375

Reorder the terms:
-0.375 + 0.375 + -2.3125x + x2 = 0 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + -2.3125x + x2 = 0 + 0.375
-2.3125x + x2 = 0 + 0.375

Combine like terms: 0 + 0.375 = 0.375
-2.3125x + x2 = 0.375

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 = 0.375 + 1.336914063

Reorder the terms:
1.336914063 + -2.3125x + x2 = 0.375 + 1.336914063

Combine like terms: 0.375 + 1.336914063 = 1.711914063
1.336914063 + -2.3125x + x2 = 1.711914063

Factor a perfect square on the left side:
(x + -1.15625)(x + -1.15625) = 1.711914063

Calculate the square root of the right side: 1.308401339

Break this problem into two subproblems by setting 
(x + -1.15625) equal to 1.308401339 and -1.308401339.

Subproblem 1
x + -1.15625 = 1.308401339

Simplifying
x + -1.15625 = 1.308401339

Reorder the terms:
-1.15625 + x = 1.308401339

Solving
-1.15625 + x = 1.308401339

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 = 1.308401339 + 1.15625

Combine like terms: -1.15625 + 1.15625 = 0.00000
0.00000 + x = 1.308401339 + 1.15625
x = 1.308401339 + 1.15625

Combine like terms: 1.308401339 + 1.15625 = 2.464651339
x = 2.464651339

Simplifying
x = 2.464651339

Subproblem 2
x + -1.15625 = -1.308401339

Simplifying
x + -1.15625 = -1.308401339

Reorder the terms:
-1.15625 + x = -1.308401339

Solving
-1.15625 + x = -1.308401339

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 = -1.308401339 + 1.15625

Combine like terms: -1.15625 + 1.15625 = 0.00000
0.00000 + x = -1.308401339 + 1.15625
x = -1.308401339 + 1.15625

Combine like terms: -1.308401339 + 1.15625 = -0.152151339
x = -0.152151339

Simplifying
x = -0.152151339

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.464651339, -0.152151339}