-7x^2+71x-2=0

Solution for -7x^2+71x-2=0 equation:

Simplifying
-7x2 + 71x + -2 = 0

Reorder the terms:
-2 + 71x + -7x2 = 0

Solving
-2 + 71x + -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 + -10.14285714x + x2 = 0

Move the constant term to the right:

Add '-0.2857142857' to each side of the equation.
0.2857142857 + -10.14285714x + -0.2857142857 + x2 = 0 + -0.2857142857

Reorder the terms:
0.2857142857 + -0.2857142857 + -10.14285714x + x2 = 0 + -0.2857142857

Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000
0.0000000000 + -10.14285714x + x2 = 0 + -0.2857142857
-10.14285714x + x2 = 0 + -0.2857142857

Combine like terms: 0 + -0.2857142857 = -0.2857142857
-10.14285714x + x2 = -0.2857142857

The x term is -10.14285714x.  Take half its coefficient (-5.07142857).
Square it (25.71938774) and add it to both sides.

Add '25.71938774' to each side of the equation.
-10.14285714x + 25.71938774 + x2 = -0.2857142857 + 25.71938774

Reorder the terms:
25.71938774 + -10.14285714x + x2 = -0.2857142857 + 25.71938774

Combine like terms: -0.2857142857 + 25.71938774 = 25.4336734543
25.71938774 + -10.14285714x + x2 = 25.4336734543

Factor a perfect square on the left side:
(x + -5.07142857)(x + -5.07142857) = 25.4336734543

Calculate the square root of the right side: 5.043180887

Break this problem into two subproblems by setting 
(x + -5.07142857) equal to 5.043180887 and -5.043180887.

Subproblem 1
x + -5.07142857 = 5.043180887

Simplifying
x + -5.07142857 = 5.043180887

Reorder the terms:
-5.07142857 + x = 5.043180887

Solving
-5.07142857 + x = 5.043180887

Solving for variable 'x'.

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

Add '5.07142857' to each side of the equation.
-5.07142857 + 5.07142857 + x = 5.043180887 + 5.07142857

Combine like terms: -5.07142857 + 5.07142857 = 0.00000000
0.00000000 + x = 5.043180887 + 5.07142857
x = 5.043180887 + 5.07142857

Combine like terms: 5.043180887 + 5.07142857 = 10.114609457
x = 10.114609457

Simplifying
x = 10.114609457

Subproblem 2
x + -5.07142857 = -5.043180887

Simplifying
x + -5.07142857 = -5.043180887

Reorder the terms:
-5.07142857 + x = -5.043180887

Solving
-5.07142857 + x = -5.043180887

Solving for variable 'x'.

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

Add '5.07142857' to each side of the equation.
-5.07142857 + 5.07142857 + x = -5.043180887 + 5.07142857

Combine like terms: -5.07142857 + 5.07142857 = 0.00000000
0.00000000 + x = -5.043180887 + 5.07142857
x = -5.043180887 + 5.07142857

Combine like terms: -5.043180887 + 5.07142857 = 0.028247683
x = 0.028247683

Simplifying
x = 0.028247683

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.114609457, 0.028247683}