7x^2-16x-8=0

Solution for 7x^2-16x-8=0 equation:

Simplifying
7x2 + -16x + -8 = 0

Reorder the terms:
-8 + -16x + 7x2 = 0

Solving
-8 + -16x + 7x2 = 0

Solving for variable 'x'.

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

Divide each side by '7'.
-1.142857143 + -2.285714286x + x2 = 0

Move the constant term to the right:

Add '1.142857143' to each side of the equation.
-1.142857143 + -2.285714286x + 1.142857143 + x2 = 0 + 1.142857143

Reorder the terms:
-1.142857143 + 1.142857143 + -2.285714286x + x2 = 0 + 1.142857143

Combine like terms: -1.142857143 + 1.142857143 = 0.000000000
0.000000000 + -2.285714286x + x2 = 0 + 1.142857143
-2.285714286x + x2 = 0 + 1.142857143

Combine like terms: 0 + 1.142857143 = 1.142857143
-2.285714286x + x2 = 1.142857143

The x term is -2.285714286x.  Take half its coefficient (-1.142857143).
Square it (1.306122449) and add it to both sides.

Add '1.306122449' to each side of the equation.
-2.285714286x + 1.306122449 + x2 = 1.142857143 + 1.306122449

Reorder the terms:
1.306122449 + -2.285714286x + x2 = 1.142857143 + 1.306122449

Combine like terms: 1.142857143 + 1.306122449 = 2.448979592
1.306122449 + -2.285714286x + x2 = 2.448979592

Factor a perfect square on the left side:
(x + -1.142857143)(x + -1.142857143) = 2.448979592

Calculate the square root of the right side: 1.564921593

Break this problem into two subproblems by setting 
(x + -1.142857143) equal to 1.564921593 and -1.564921593.

Subproblem 1
x + -1.142857143 = 1.564921593

Simplifying
x + -1.142857143 = 1.564921593

Reorder the terms:
-1.142857143 + x = 1.564921593

Solving
-1.142857143 + x = 1.564921593

Solving for variable 'x'.

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

Add '1.142857143' to each side of the equation.
-1.142857143 + 1.142857143 + x = 1.564921593 + 1.142857143

Combine like terms: -1.142857143 + 1.142857143 = 0.000000000
0.000000000 + x = 1.564921593 + 1.142857143
x = 1.564921593 + 1.142857143

Combine like terms: 1.564921593 + 1.142857143 = 2.707778736
x = 2.707778736

Simplifying
x = 2.707778736

Subproblem 2
x + -1.142857143 = -1.564921593

Simplifying
x + -1.142857143 = -1.564921593

Reorder the terms:
-1.142857143 + x = -1.564921593

Solving
-1.142857143 + x = -1.564921593

Solving for variable 'x'.

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

Add '1.142857143' to each side of the equation.
-1.142857143 + 1.142857143 + x = -1.564921593 + 1.142857143

Combine like terms: -1.142857143 + 1.142857143 = 0.000000000
0.000000000 + x = -1.564921593 + 1.142857143
x = -1.564921593 + 1.142857143

Combine like terms: -1.564921593 + 1.142857143 = -0.42206445
x = -0.42206445

Simplifying
x = -0.42206445

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.707778736, -0.42206445}