16x^2+28x+14=6

Solution for 16x^2+28x+14=6 equation:

Simplifying
16x2 + 28x + 14 = 6

Reorder the terms:
14 + 28x + 16x2 = 6

Solving
14 + 28x + 16x2 = 6

Solving for variable 'x'.

Reorder the terms:
14 + -6 + 28x + 16x2 = 6 + -6

Combine like terms: 14 + -6 = 8
8 + 28x + 16x2 = 6 + -6

Combine like terms: 6 + -6 = 0
8 + 28x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(2 + 7x + 4x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(2 + 7x + 4x2)' equal to zero and attempt to solve:

Simplifying
2 + 7x + 4x2 = 0

Solving
2 + 7x + 4x2 = 0

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

Divide each side by '4'.
0.5 + 1.75x + x2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + 1.75x + -0.5 + x2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + 1.75x + x2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + 1.75x + x2 = 0 + -0.5
1.75x + x2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
1.75x + x2 = -0.5

The x term is 1.75x.  Take half its coefficient (0.875).
Square it (0.765625) and add it to both sides.

Add '0.765625' to each side of the equation.
1.75x + 0.765625 + x2 = -0.5 + 0.765625

Reorder the terms:
0.765625 + 1.75x + x2 = -0.5 + 0.765625

Combine like terms: -0.5 + 0.765625 = 0.265625
0.765625 + 1.75x + x2 = 0.265625

Factor a perfect square on the left side:
(x + 0.875)(x + 0.875) = 0.265625

Calculate the square root of the right side: 0.515388203

Break this problem into two subproblems by setting 
(x + 0.875) equal to 0.515388203 and -0.515388203.

Subproblem 1
x + 0.875 = 0.515388203

Simplifying
x + 0.875 = 0.515388203

Reorder the terms:
0.875 + x = 0.515388203

Solving
0.875 + x = 0.515388203

Solving for variable 'x'.

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

Add '-0.875' to each side of the equation.
0.875 + -0.875 + x = 0.515388203 + -0.875

Combine like terms: 0.875 + -0.875 = 0.000
0.000 + x = 0.515388203 + -0.875
x = 0.515388203 + -0.875

Combine like terms: 0.515388203 + -0.875 = -0.359611797
x = -0.359611797

Simplifying
x = -0.359611797

Subproblem 2
x + 0.875 = -0.515388203

Simplifying
x + 0.875 = -0.515388203

Reorder the terms:
0.875 + x = -0.515388203

Solving
0.875 + x = -0.515388203

Solving for variable 'x'.

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

Add '-0.875' to each side of the equation.
0.875 + -0.875 + x = -0.515388203 + -0.875

Combine like terms: 0.875 + -0.875 = 0.000
0.000 + x = -0.515388203 + -0.875
x = -0.515388203 + -0.875

Combine like terms: -0.515388203 + -0.875 = -1.390388203
x = -1.390388203

Simplifying
x = -1.390388203

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.359611797, -1.390388203}
Solution
x = {-0.359611797, -1.390388203}