16q^2+8q+1=12

Solution for 16q^2+8q+1=12 equation:

Simplifying
16q2 + 8q + 1 = 12

Reorder the terms:
1 + 8q + 16q2 = 12

Solving
1 + 8q + 16q2 = 12

Solving for variable 'q'.

Reorder the terms:
1 + -12 + 8q + 16q2 = 12 + -12

Combine like terms: 1 + -12 = -11
-11 + 8q + 16q2 = 12 + -12

Combine like terms: 12 + -12 = 0
-11 + 8q + 16q2 = 0

Begin completing the square.  Divide all terms by
16 the coefficient of the squared term: 

Divide each side by '16'.
-0.6875 + 0.5q + q2 = 0

Move the constant term to the right:

Add '0.6875' to each side of the equation.
-0.6875 + 0.5q + 0.6875 + q2 = 0 + 0.6875

Reorder the terms:
-0.6875 + 0.6875 + 0.5q + q2 = 0 + 0.6875

Combine like terms: -0.6875 + 0.6875 = 0.0000
0.0000 + 0.5q + q2 = 0 + 0.6875
0.5q + q2 = 0 + 0.6875

Combine like terms: 0 + 0.6875 = 0.6875
0.5q + q2 = 0.6875

The q term is 0.5q.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5q + 0.0625 + q2 = 0.6875 + 0.0625

Reorder the terms:
0.0625 + 0.5q + q2 = 0.6875 + 0.0625

Combine like terms: 0.6875 + 0.0625 = 0.75
0.0625 + 0.5q + q2 = 0.75

Factor a perfect square on the left side:
(q + 0.25)(q + 0.25) = 0.75

Calculate the square root of the right side: 0.866025404

Break this problem into two subproblems by setting 
(q + 0.25) equal to 0.866025404 and -0.866025404.

Subproblem 1
q + 0.25 = 0.866025404

Simplifying
q + 0.25 = 0.866025404

Reorder the terms:
0.25 + q = 0.866025404

Solving
0.25 + q = 0.866025404

Solving for variable 'q'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + q = 0.866025404 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + q = 0.866025404 + -0.25
q = 0.866025404 + -0.25

Combine like terms: 0.866025404 + -0.25 = 0.616025404
q = 0.616025404

Simplifying
q = 0.616025404

Subproblem 2
q + 0.25 = -0.866025404

Simplifying
q + 0.25 = -0.866025404

Reorder the terms:
0.25 + q = -0.866025404

Solving
0.25 + q = -0.866025404

Solving for variable 'q'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + q = -0.866025404 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + q = -0.866025404 + -0.25
q = -0.866025404 + -0.25

Combine like terms: -0.866025404 + -0.25 = -1.116025404
q = -1.116025404

Simplifying
q = -1.116025404

Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {0.616025404, -1.116025404}