16x^2+6x-3=0

Solution for 16x^2+6x-3=0 equation:

Simplifying
16x2 + 6x + -3 = 0

Reorder the terms:
-3 + 6x + 16x2 = 0

Solving
-3 + 6x + 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'.
-0.1875 + 0.375x + x2 = 0

Move the constant term to the right:

Add '0.1875' to each side of the equation.
-0.1875 + 0.375x + 0.1875 + x2 = 0 + 0.1875

Reorder the terms:
-0.1875 + 0.1875 + 0.375x + x2 = 0 + 0.1875

Combine like terms: -0.1875 + 0.1875 = 0.0000
0.0000 + 0.375x + x2 = 0 + 0.1875
0.375x + x2 = 0 + 0.1875

Combine like terms: 0 + 0.1875 = 0.1875
0.375x + x2 = 0.1875

The x term is 0.375x.  Take half its coefficient (0.1875).
Square it (0.03515625) and add it to both sides.

Add '0.03515625' to each side of the equation.
0.375x + 0.03515625 + x2 = 0.1875 + 0.03515625

Reorder the terms:
0.03515625 + 0.375x + x2 = 0.1875 + 0.03515625

Combine like terms: 0.1875 + 0.03515625 = 0.22265625
0.03515625 + 0.375x + x2 = 0.22265625

Factor a perfect square on the left side:
(x + 0.1875)(x + 0.1875) = 0.22265625

Calculate the square root of the right side: 0.471864652

Break this problem into two subproblems by setting 
(x + 0.1875) equal to 0.471864652 and -0.471864652.

Subproblem 1
x + 0.1875 = 0.471864652

Simplifying
x + 0.1875 = 0.471864652

Reorder the terms:
0.1875 + x = 0.471864652

Solving
0.1875 + x = 0.471864652

Solving for variable 'x'.

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

Add '-0.1875' to each side of the equation.
0.1875 + -0.1875 + x = 0.471864652 + -0.1875

Combine like terms: 0.1875 + -0.1875 = 0.0000
0.0000 + x = 0.471864652 + -0.1875
x = 0.471864652 + -0.1875

Combine like terms: 0.471864652 + -0.1875 = 0.284364652
x = 0.284364652

Simplifying
x = 0.284364652

Subproblem 2
x + 0.1875 = -0.471864652

Simplifying
x + 0.1875 = -0.471864652

Reorder the terms:
0.1875 + x = -0.471864652

Solving
0.1875 + x = -0.471864652

Solving for variable 'x'.

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

Add '-0.1875' to each side of the equation.
0.1875 + -0.1875 + x = -0.471864652 + -0.1875

Combine like terms: 0.1875 + -0.1875 = 0.0000
0.0000 + x = -0.471864652 + -0.1875
x = -0.471864652 + -0.1875

Combine like terms: -0.471864652 + -0.1875 = -0.659364652
x = -0.659364652

Simplifying
x = -0.659364652

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.284364652, -0.659364652}