16x^2-7x-5=0

Solution for 16x^2-7x-5=0 equation:

Simplifying
16x2 + -7x + -5 = 0

Reorder the terms:
-5 + -7x + 16x2 = 0

Solving
-5 + -7x + 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'.
-0.3125 + -0.4375x + x2 = 0

Move the constant term to the right:

Add '0.3125' to each side of the equation.
-0.3125 + -0.4375x + 0.3125 + x2 = 0 + 0.3125

Reorder the terms:
-0.3125 + 0.3125 + -0.4375x + x2 = 0 + 0.3125

Combine like terms: -0.3125 + 0.3125 = 0.0000
0.0000 + -0.4375x + x2 = 0 + 0.3125
-0.4375x + x2 = 0 + 0.3125

Combine like terms: 0 + 0.3125 = 0.3125
-0.4375x + x2 = 0.3125

The x term is -0.4375x.  Take half its coefficient (-0.21875).
Square it (0.0478515625) and add it to both sides.

Add '0.0478515625' to each side of the equation.
-0.4375x + 0.0478515625 + x2 = 0.3125 + 0.0478515625

Reorder the terms:
0.0478515625 + -0.4375x + x2 = 0.3125 + 0.0478515625

Combine like terms: 0.3125 + 0.0478515625 = 0.3603515625
0.0478515625 + -0.4375x + x2 = 0.3603515625

Factor a perfect square on the left side:
(x + -0.21875)(x + -0.21875) = 0.3603515625

Calculate the square root of the right side: 0.600292897

Break this problem into two subproblems by setting 
(x + -0.21875) equal to 0.600292897 and -0.600292897.

Subproblem 1
x + -0.21875 = 0.600292897

Simplifying
x + -0.21875 = 0.600292897

Reorder the terms:
-0.21875 + x = 0.600292897

Solving
-0.21875 + x = 0.600292897

Solving for variable 'x'.

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

Add '0.21875' to each side of the equation.
-0.21875 + 0.21875 + x = 0.600292897 + 0.21875

Combine like terms: -0.21875 + 0.21875 = 0.00000
0.00000 + x = 0.600292897 + 0.21875
x = 0.600292897 + 0.21875

Combine like terms: 0.600292897 + 0.21875 = 0.819042897
x = 0.819042897

Simplifying
x = 0.819042897

Subproblem 2
x + -0.21875 = -0.600292897

Simplifying
x + -0.21875 = -0.600292897

Reorder the terms:
-0.21875 + x = -0.600292897

Solving
-0.21875 + x = -0.600292897

Solving for variable 'x'.

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

Add '0.21875' to each side of the equation.
-0.21875 + 0.21875 + x = -0.600292897 + 0.21875

Combine like terms: -0.21875 + 0.21875 = 0.00000
0.00000 + x = -0.600292897 + 0.21875
x = -0.600292897 + 0.21875

Combine like terms: -0.600292897 + 0.21875 = -0.381542897
x = -0.381542897

Simplifying
x = -0.381542897

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.819042897, -0.381542897}