7x^2+17x-2=0

Solution for 7x^2+17x-2=0 equation:

Simplifying
7x2 + 17x + -2 = 0

Reorder the terms:
-2 + 17x + 7x2 = 0

Solving
-2 + 17x + 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 + 2.428571429x + x2 = 0

Move the constant term to the right:

Add '0.2857142857' to each side of the equation.
-0.2857142857 + 2.428571429x + 0.2857142857 + x2 = 0 + 0.2857142857

Reorder the terms:
-0.2857142857 + 0.2857142857 + 2.428571429x + x2 = 0 + 0.2857142857

Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000
0.0000000000 + 2.428571429x + x2 = 0 + 0.2857142857
2.428571429x + x2 = 0 + 0.2857142857

Combine like terms: 0 + 0.2857142857 = 0.2857142857
2.428571429x + x2 = 0.2857142857

The x term is 2.428571429x.  Take half its coefficient (1.214285715).
Square it (1.474489798) and add it to both sides.

Add '1.474489798' to each side of the equation.
2.428571429x + 1.474489798 + x2 = 0.2857142857 + 1.474489798

Reorder the terms:
1.474489798 + 2.428571429x + x2 = 0.2857142857 + 1.474489798

Combine like terms: 0.2857142857 + 1.474489798 = 1.7602040837
1.474489798 + 2.428571429x + x2 = 1.7602040837

Factor a perfect square on the left side:
(x + 1.214285715)(x + 1.214285715) = 1.7602040837

Calculate the square root of the right side: 1.326726831

Break this problem into two subproblems by setting 
(x + 1.214285715) equal to 1.326726831 and -1.326726831.

Subproblem 1
x + 1.214285715 = 1.326726831

Simplifying
x + 1.214285715 = 1.326726831

Reorder the terms:
1.214285715 + x = 1.326726831

Solving
1.214285715 + x = 1.326726831

Solving for variable 'x'.

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

Add '-1.214285715' to each side of the equation.
1.214285715 + -1.214285715 + x = 1.326726831 + -1.214285715

Combine like terms: 1.214285715 + -1.214285715 = 0.000000000
0.000000000 + x = 1.326726831 + -1.214285715
x = 1.326726831 + -1.214285715

Combine like terms: 1.326726831 + -1.214285715 = 0.112441116
x = 0.112441116

Simplifying
x = 0.112441116

Subproblem 2
x + 1.214285715 = -1.326726831

Simplifying
x + 1.214285715 = -1.326726831

Reorder the terms:
1.214285715 + x = -1.326726831

Solving
1.214285715 + x = -1.326726831

Solving for variable 'x'.

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

Add '-1.214285715' to each side of the equation.
1.214285715 + -1.214285715 + x = -1.326726831 + -1.214285715

Combine like terms: 1.214285715 + -1.214285715 = 0.000000000
0.000000000 + x = -1.326726831 + -1.214285715
x = -1.326726831 + -1.214285715

Combine like terms: -1.326726831 + -1.214285715 = -2.541012546
x = -2.541012546

Simplifying
x = -2.541012546

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.112441116, -2.541012546}