(5x^2)+13x-1=0

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Solution for (5x^2)+13x-1=0 equation:


Simplifying
(5x2) + 13x + -1 = 0

Reorder the terms:
-1 + 13x + (5x2) = 0

Solving
-1 + 13x + (5x2) = 0

Solving for variable 'x'.

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

Divide each side by '5'.
-0.2 + 2.6x + x2 = 0

Move the constant term to the right:

Add '0.2' to each side of the equation.
-0.2 + 2.6x + 0.2 + x2 = 0 + 0.2

Reorder the terms:
-0.2 + 0.2 + 2.6x + x2 = 0 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + 2.6x + x2 = 0 + 0.2
2.6x + x2 = 0 + 0.2

Combine like terms: 0 + 0.2 = 0.2
2.6x + x2 = 0.2

The x term is 2.6x.  Take half its coefficient (1.3).
Square it (1.69) and add it to both sides.

Add '1.69' to each side of the equation.
2.6x + 1.69 + x2 = 0.2 + 1.69

Reorder the terms:
1.69 + 2.6x + x2 = 0.2 + 1.69

Combine like terms: 0.2 + 1.69 = 1.89
1.69 + 2.6x + x2 = 1.89

Factor a perfect square on the left side:
((x) + 1.3)((x) + 1.3) = 1.89

Calculate the square root of the right side: 1.374772708

Break this problem into two subproblems by setting 
((x) + 1.3) equal to 1.374772708 and -1.374772708.

Subproblem 1

(x) + 1.3 = 1.374772708 Simplifying (x) + 1.3 = 1.374772708 x + 1.3 = 1.374772708 Reorder the terms: 1.3 + x = 1.374772708 Solving 1.3 + x = 1.374772708 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.3' to each side of the equation. 1.3 + -1.3 + x = 1.374772708 + -1.3 Combine like terms: 1.3 + -1.3 = 0.0 0.0 + x = 1.374772708 + -1.3 x = 1.374772708 + -1.3 Combine like terms: 1.374772708 + -1.3 = 0.074772708 x = 0.074772708 Simplifying x = 0.074772708

Subproblem 2

(x) + 1.3 = -1.374772708 Simplifying (x) + 1.3 = -1.374772708 x + 1.3 = -1.374772708 Reorder the terms: 1.3 + x = -1.374772708 Solving 1.3 + x = -1.374772708 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.3' to each side of the equation. 1.3 + -1.3 + x = -1.374772708 + -1.3 Combine like terms: 1.3 + -1.3 = 0.0 0.0 + x = -1.374772708 + -1.3 x = -1.374772708 + -1.3 Combine like terms: -1.374772708 + -1.3 = -2.674772708 x = -2.674772708 Simplifying x = -2.674772708

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.074772708, -2.674772708}

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