16x^2+14x-16=0

Solution for 16x^2+14x-16=0 equation:

Simplifying
16x2 + 14x + -16 = 0

Reorder the terms:
-16 + 14x + 16x2 = 0

Solving
-16 + 14x + 16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-8 + 7x + 8x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-8 + 7x + 8x2)' equal to zero and attempt to solve:

Simplifying
-8 + 7x + 8x2 = 0

Solving
-8 + 7x + 8x2 = 0

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

Divide each side by '8'.
-1 + 0.875x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 0.875x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + 0.875x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 0.875x + x2 = 0 + 1
0.875x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
0.875x + x2 = 1

The x term is 0.875x.  Take half its coefficient (0.4375).
Square it (0.19140625) and add it to both sides.

Add '0.19140625' to each side of the equation.
0.875x + 0.19140625 + x2 = 1 + 0.19140625

Reorder the terms:
0.19140625 + 0.875x + x2 = 1 + 0.19140625

Combine like terms: 1 + 0.19140625 = 1.19140625
0.19140625 + 0.875x + x2 = 1.19140625

Factor a perfect square on the left side:
(x + 0.4375)(x + 0.4375) = 1.19140625

Calculate the square root of the right side: 1.091515575

Break this problem into two subproblems by setting 
(x + 0.4375) equal to 1.091515575 and -1.091515575.

Subproblem 1
x + 0.4375 = 1.091515575

Simplifying
x + 0.4375 = 1.091515575

Reorder the terms:
0.4375 + x = 1.091515575

Solving
0.4375 + x = 1.091515575

Solving for variable 'x'.

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

Add '-0.4375' to each side of the equation.
0.4375 + -0.4375 + x = 1.091515575 + -0.4375

Combine like terms: 0.4375 + -0.4375 = 0.0000
0.0000 + x = 1.091515575 + -0.4375
x = 1.091515575 + -0.4375

Combine like terms: 1.091515575 + -0.4375 = 0.654015575
x = 0.654015575

Simplifying
x = 0.654015575

Subproblem 2
x + 0.4375 = -1.091515575

Simplifying
x + 0.4375 = -1.091515575

Reorder the terms:
0.4375 + x = -1.091515575

Solving
0.4375 + x = -1.091515575

Solving for variable 'x'.

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

Add '-0.4375' to each side of the equation.
0.4375 + -0.4375 + x = -1.091515575 + -0.4375

Combine like terms: 0.4375 + -0.4375 = 0.0000
0.0000 + x = -1.091515575 + -0.4375
x = -1.091515575 + -0.4375

Combine like terms: -1.091515575 + -0.4375 = -1.529015575
x = -1.529015575

Simplifying
x = -1.529015575

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.654015575, -1.529015575}
Solution
x = {0.654015575, -1.529015575}