16x^2+x-1=0

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

Simplifying
16x2 + x + -1 = 0

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

Solving
-1 + x + 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 + 0.0625x + x2 = 0

Move the constant term to the right:

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

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

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

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

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.0625x + 0.25 + x2 = 0.0625 + 0.25

Reorder the terms:
0.25 + 0.0625x + x2 = 0.0625 + 0.25

Combine like terms: 0.0625 + 0.25 = 0.3125
0.25 + 0.0625x + x2 = 0.3125

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 0.3125

Calculate the square root of the right side: 0.559016994

Break this problem into two subproblems by setting 
(x + 0.5) equal to 0.559016994 and -0.559016994.

Subproblem 1
x + 0.5 = 0.559016994

Simplifying
x + 0.5 = 0.559016994

Reorder the terms:
0.5 + x = 0.559016994

Solving
0.5 + x = 0.559016994

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 0.559016994 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 0.559016994 + -0.5
x = 0.559016994 + -0.5

Combine like terms: 0.559016994 + -0.5 = 0.059016994
x = 0.059016994

Simplifying
x = 0.059016994

Subproblem 2
x + 0.5 = -0.559016994

Simplifying
x + 0.5 = -0.559016994

Reorder the terms:
0.5 + x = -0.559016994

Solving
0.5 + x = -0.559016994

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -0.559016994 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -0.559016994 + -0.5
x = -0.559016994 + -0.5

Combine like terms: -0.559016994 + -0.5 = -1.059016994
x = -1.059016994

Simplifying
x = -1.059016994

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.059016994, -1.059016994}