13x^2+2x-2=0

Solution for 13x^2+2x-2=0 equation:

Simplifying
13x2 + 2x + -2 = 0

Reorder the terms:
-2 + 2x + 13x2 = 0

Solving
-2 + 2x + 13x2 = 0

Solving for variable 'x'.

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

Divide each side by '13'.
-0.1538461538 + 0.1538461538x + x2 = 0

Move the constant term to the right:

Add '0.1538461538' to each side of the equation.
-0.1538461538 + 0.1538461538x + 0.1538461538 + x2 = 0 + 0.1538461538

Reorder the terms:
-0.1538461538 + 0.1538461538 + 0.1538461538x + x2 = 0 + 0.1538461538

Combine like terms: -0.1538461538 + 0.1538461538 = 0.0000000000
0.0000000000 + 0.1538461538x + x2 = 0 + 0.1538461538
0.1538461538x + x2 = 0 + 0.1538461538

Combine like terms: 0 + 0.1538461538 = 0.1538461538
0.1538461538x + x2 = 0.1538461538

The x term is 0.1538461538x.  Take half its coefficient (0.0769230769).
Square it (0.005917159760) and add it to both sides.

Add '0.005917159760' to each side of the equation.
0.1538461538x + 0.005917159760 + x2 = 0.1538461538 + 0.005917159760

Reorder the terms:
0.005917159760 + 0.1538461538x + x2 = 0.1538461538 + 0.005917159760

Combine like terms: 0.1538461538 + 0.005917159760 = 0.15976331356
0.005917159760 + 0.1538461538x + x2 = 0.15976331356

Factor a perfect square on the left side:
(x + 0.0769230769)(x + 0.0769230769) = 0.15976331356

Calculate the square root of the right side: 0.399704032

Break this problem into two subproblems by setting 
(x + 0.0769230769) equal to 0.399704032 and -0.399704032.

Subproblem 1
x + 0.0769230769 = 0.399704032

Simplifying
x + 0.0769230769 = 0.399704032

Reorder the terms:
0.0769230769 + x = 0.399704032

Solving
0.0769230769 + x = 0.399704032

Solving for variable 'x'.

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

Add '-0.0769230769' to each side of the equation.
0.0769230769 + -0.0769230769 + x = 0.399704032 + -0.0769230769

Combine like terms: 0.0769230769 + -0.0769230769 = 0.0000000000
0.0000000000 + x = 0.399704032 + -0.0769230769
x = 0.399704032 + -0.0769230769

Combine like terms: 0.399704032 + -0.0769230769 = 0.3227809551
x = 0.3227809551

Simplifying
x = 0.3227809551

Subproblem 2
x + 0.0769230769 = -0.399704032

Simplifying
x + 0.0769230769 = -0.399704032

Reorder the terms:
0.0769230769 + x = -0.399704032

Solving
0.0769230769 + x = -0.399704032

Solving for variable 'x'.

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

Add '-0.0769230769' to each side of the equation.
0.0769230769 + -0.0769230769 + x = -0.399704032 + -0.0769230769

Combine like terms: 0.0769230769 + -0.0769230769 = 0.0000000000
0.0000000000 + x = -0.399704032 + -0.0769230769
x = -0.399704032 + -0.0769230769

Combine like terms: -0.399704032 + -0.0769230769 = -0.4766271089
x = -0.4766271089

Simplifying
x = -0.4766271089

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.3227809551, -0.4766271089}