13x^2-7x-2=0

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Solution for 13x^2-7x-2=0 equation:


Simplifying
13x2 + -7x + -2 = 0

Reorder the terms:
-2 + -7x + 13x2 = 0

Solving
-2 + -7x + 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 + -0.5384615385x + x2 = 0

Move the constant term to the right:

Add '0.1538461538' to each side of the equation.
-0.1538461538 + -0.5384615385x + 0.1538461538 + x2 = 0 + 0.1538461538

Reorder the terms:
-0.1538461538 + 0.1538461538 + -0.5384615385x + x2 = 0 + 0.1538461538

Combine like terms: -0.1538461538 + 0.1538461538 = 0.0000000000
0.0000000000 + -0.5384615385x + x2 = 0 + 0.1538461538
-0.5384615385x + x2 = 0 + 0.1538461538

Combine like terms: 0 + 0.1538461538 = 0.1538461538
-0.5384615385x + x2 = 0.1538461538

The x term is -0.5384615385x.  Take half its coefficient (-0.2692307693).
Square it (0.07248520714) and add it to both sides.

Add '0.07248520714' to each side of the equation.
-0.5384615385x + 0.07248520714 + x2 = 0.1538461538 + 0.07248520714

Reorder the terms:
0.07248520714 + -0.5384615385x + x2 = 0.1538461538 + 0.07248520714

Combine like terms: 0.1538461538 + 0.07248520714 = 0.22633136094
0.07248520714 + -0.5384615385x + x2 = 0.22633136094

Factor a perfect square on the left side:
(x + -0.2692307693)(x + -0.2692307693) = 0.22633136094

Calculate the square root of the right side: 0.475742957

Break this problem into two subproblems by setting 
(x + -0.2692307693) equal to 0.475742957 and -0.475742957.

Subproblem 1

x + -0.2692307693 = 0.475742957 Simplifying x + -0.2692307693 = 0.475742957 Reorder the terms: -0.2692307693 + x = 0.475742957 Solving -0.2692307693 + x = 0.475742957 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2692307693' to each side of the equation. -0.2692307693 + 0.2692307693 + x = 0.475742957 + 0.2692307693 Combine like terms: -0.2692307693 + 0.2692307693 = 0.0000000000 0.0000000000 + x = 0.475742957 + 0.2692307693 x = 0.475742957 + 0.2692307693 Combine like terms: 0.475742957 + 0.2692307693 = 0.7449737263 x = 0.7449737263 Simplifying x = 0.7449737263

Subproblem 2

x + -0.2692307693 = -0.475742957 Simplifying x + -0.2692307693 = -0.475742957 Reorder the terms: -0.2692307693 + x = -0.475742957 Solving -0.2692307693 + x = -0.475742957 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2692307693' to each side of the equation. -0.2692307693 + 0.2692307693 + x = -0.475742957 + 0.2692307693 Combine like terms: -0.2692307693 + 0.2692307693 = 0.0000000000 0.0000000000 + x = -0.475742957 + 0.2692307693 x = -0.475742957 + 0.2692307693 Combine like terms: -0.475742957 + 0.2692307693 = -0.2065121877 x = -0.2065121877 Simplifying x = -0.2065121877

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.7449737263, -0.2065121877}

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