16x^2+138x-140=0

Solution for 16x^2+138x-140=0 equation:

Simplifying
16x2 + 138x + -140 = 0

Reorder the terms:
-140 + 138x + 16x2 = 0

Solving
-140 + 138x + 16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-70 + 69x + 8x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-70 + 69x + 8x2)' equal to zero and attempt to solve:

Simplifying
-70 + 69x + 8x2 = 0

Solving
-70 + 69x + 8x2 = 0

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

Divide each side by '8'.
-8.75 + 8.625x + x2 = 0

Move the constant term to the right:

Add '8.75' to each side of the equation.
-8.75 + 8.625x + 8.75 + x2 = 0 + 8.75

Reorder the terms:
-8.75 + 8.75 + 8.625x + x2 = 0 + 8.75

Combine like terms: -8.75 + 8.75 = 0.00
0.00 + 8.625x + x2 = 0 + 8.75
8.625x + x2 = 0 + 8.75

Combine like terms: 0 + 8.75 = 8.75
8.625x + x2 = 8.75

The x term is 8.625x.  Take half its coefficient (4.3125).
Square it (18.59765625) and add it to both sides.

Add '18.59765625' to each side of the equation.
8.625x + 18.59765625 + x2 = 8.75 + 18.59765625

Reorder the terms:
18.59765625 + 8.625x + x2 = 8.75 + 18.59765625

Combine like terms: 8.75 + 18.59765625 = 27.34765625
18.59765625 + 8.625x + x2 = 27.34765625

Factor a perfect square on the left side:
(x + 4.3125)(x + 4.3125) = 27.34765625

Calculate the square root of the right side: 5.229498661

Break this problem into two subproblems by setting 
(x + 4.3125) equal to 5.229498661 and -5.229498661.

Subproblem 1
x + 4.3125 = 5.229498661

Simplifying
x + 4.3125 = 5.229498661

Reorder the terms:
4.3125 + x = 5.229498661

Solving
4.3125 + x = 5.229498661

Solving for variable 'x'.

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

Add '-4.3125' to each side of the equation.
4.3125 + -4.3125 + x = 5.229498661 + -4.3125

Combine like terms: 4.3125 + -4.3125 = 0.0000
0.0000 + x = 5.229498661 + -4.3125
x = 5.229498661 + -4.3125

Combine like terms: 5.229498661 + -4.3125 = 0.916998661
x = 0.916998661

Simplifying
x = 0.916998661

Subproblem 2
x + 4.3125 = -5.229498661

Simplifying
x + 4.3125 = -5.229498661

Reorder the terms:
4.3125 + x = -5.229498661

Solving
4.3125 + x = -5.229498661

Solving for variable 'x'.

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

Add '-4.3125' to each side of the equation.
4.3125 + -4.3125 + x = -5.229498661 + -4.3125

Combine like terms: 4.3125 + -4.3125 = 0.0000
0.0000 + x = -5.229498661 + -4.3125
x = -5.229498661 + -4.3125

Combine like terms: -5.229498661 + -4.3125 = -9.541998661
x = -9.541998661

Simplifying
x = -9.541998661

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.916998661, -9.541998661}
Solution
x = {0.916998661, -9.541998661}