-7x^2+16x-2=0

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

Simplifying
-7x2 + 16x + -2 = 0

Reorder the terms:
-2 + 16x + -7x2 = 0

Solving
-2 + 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'.
0.2857142857 + -2.285714286x + x2 = 0

Move the constant term to the right:

Add '-0.2857142857' to each side of the equation.
0.2857142857 + -2.285714286x + -0.2857142857 + x2 = 0 + -0.2857142857

Reorder the terms:
0.2857142857 + -0.2857142857 + -2.285714286x + x2 = 0 + -0.2857142857

Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000
0.0000000000 + -2.285714286x + x2 = 0 + -0.2857142857
-2.285714286x + x2 = 0 + -0.2857142857

Combine like terms: 0 + -0.2857142857 = -0.2857142857
-2.285714286x + x2 = -0.2857142857

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 = -0.2857142857 + 1.306122449

Reorder the terms:
1.306122449 + -2.285714286x + x2 = -0.2857142857 + 1.306122449

Combine like terms: -0.2857142857 + 1.306122449 = 1.0204081633
1.306122449 + -2.285714286x + x2 = 1.0204081633

Factor a perfect square on the left side:
(x + -1.142857143)(x + -1.142857143) = 1.0204081633

Calculate the square root of the right side: 1.010152545

Break this problem into two subproblems by setting 
(x + -1.142857143) equal to 1.010152545 and -1.010152545.

Subproblem 1
x + -1.142857143 = 1.010152545

Simplifying
x + -1.142857143 = 1.010152545

Reorder the terms:
-1.142857143 + x = 1.010152545

Solving
-1.142857143 + x = 1.010152545

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 = 1.010152545 + 1.142857143

Combine like terms: -1.142857143 + 1.142857143 = 0.000000000
0.000000000 + x = 1.010152545 + 1.142857143
x = 1.010152545 + 1.142857143

Combine like terms: 1.010152545 + 1.142857143 = 2.153009688
x = 2.153009688

Simplifying
x = 2.153009688

Subproblem 2
x + -1.142857143 = -1.010152545

Simplifying
x + -1.142857143 = -1.010152545

Reorder the terms:
-1.142857143 + x = -1.010152545

Solving
-1.142857143 + x = -1.010152545

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 = -1.010152545 + 1.142857143

Combine like terms: -1.142857143 + 1.142857143 = 0.000000000
0.000000000 + x = -1.010152545 + 1.142857143
x = -1.010152545 + 1.142857143

Combine like terms: -1.010152545 + 1.142857143 = 0.132704598
x = 0.132704598

Simplifying
x = 0.132704598

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.153009688, 0.132704598}