16x^2+3x-1=0

Solution for 16x^2+3x-1=0 equation:

Simplifying
16x2 + 3x + -1 = 0

Reorder the terms:
-1 + 3x + 16x2 = 0

Solving
-1 + 3x + 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'.
-0.0625 + 0.1875x + x2 = 0

Move the constant term to the right:

Add '0.0625' to each side of the equation.
-0.0625 + 0.1875x + 0.0625 + x2 = 0 + 0.0625

Reorder the terms:
-0.0625 + 0.0625 + 0.1875x + x2 = 0 + 0.0625

Combine like terms: -0.0625 + 0.0625 = 0.0000
0.0000 + 0.1875x + x2 = 0 + 0.0625
0.1875x + x2 = 0 + 0.0625

Combine like terms: 0 + 0.0625 = 0.0625
0.1875x + x2 = 0.0625

The x term is 0.1875x.  Take half its coefficient (0.09375).
Square it (0.0087890625) and add it to both sides.

Add '0.0087890625' to each side of the equation.
0.1875x + 0.0087890625 + x2 = 0.0625 + 0.0087890625

Reorder the terms:
0.0087890625 + 0.1875x + x2 = 0.0625 + 0.0087890625

Combine like terms: 0.0625 + 0.0087890625 = 0.0712890625
0.0087890625 + 0.1875x + x2 = 0.0712890625

Factor a perfect square on the left side:
(x + 0.09375)(x + 0.09375) = 0.0712890625

Calculate the square root of the right side: 0.267000117

Break this problem into two subproblems by setting 
(x + 0.09375) equal to 0.267000117 and -0.267000117.

Subproblem 1
x + 0.09375 = 0.267000117

Simplifying
x + 0.09375 = 0.267000117

Reorder the terms:
0.09375 + x = 0.267000117

Solving
0.09375 + x = 0.267000117

Solving for variable 'x'.

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

Add '-0.09375' to each side of the equation.
0.09375 + -0.09375 + x = 0.267000117 + -0.09375

Combine like terms: 0.09375 + -0.09375 = 0.00000
0.00000 + x = 0.267000117 + -0.09375
x = 0.267000117 + -0.09375

Combine like terms: 0.267000117 + -0.09375 = 0.173250117
x = 0.173250117

Simplifying
x = 0.173250117

Subproblem 2
x + 0.09375 = -0.267000117

Simplifying
x + 0.09375 = -0.267000117

Reorder the terms:
0.09375 + x = -0.267000117

Solving
0.09375 + x = -0.267000117

Solving for variable 'x'.

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

Add '-0.09375' to each side of the equation.
0.09375 + -0.09375 + x = -0.267000117 + -0.09375

Combine like terms: 0.09375 + -0.09375 = 0.00000
0.00000 + x = -0.267000117 + -0.09375
x = -0.267000117 + -0.09375

Combine like terms: -0.267000117 + -0.09375 = -0.360750117
x = -0.360750117

Simplifying
x = -0.360750117

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.173250117, -0.360750117}