5r^2+13r-3=0

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Solution for 5r^2+13r-3=0 equation:


Simplifying
5r2 + 13r + -3 = 0

Reorder the terms:
-3 + 13r + 5r2 = 0

Solving
-3 + 13r + 5r2 = 0

Solving for variable 'r'.

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

Divide each side by '5'.
-0.6 + 2.6r + r2 = 0

Move the constant term to the right:

Add '0.6' to each side of the equation.
-0.6 + 2.6r + 0.6 + r2 = 0 + 0.6

Reorder the terms:
-0.6 + 0.6 + 2.6r + r2 = 0 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + 2.6r + r2 = 0 + 0.6
2.6r + r2 = 0 + 0.6

Combine like terms: 0 + 0.6 = 0.6
2.6r + r2 = 0.6

The r term is 2.6r.  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.
2.6r + 1.69 + r2 = 0.6 + 1.69

Reorder the terms:
1.69 + 2.6r + r2 = 0.6 + 1.69

Combine like terms: 0.6 + 1.69 = 2.29
1.69 + 2.6r + r2 = 2.29

Factor a perfect square on the left side:
(r + 1.3)(r + 1.3) = 2.29

Calculate the square root of the right side: 1.513274595

Break this problem into two subproblems by setting 
(r + 1.3) equal to 1.513274595 and -1.513274595.

Subproblem 1

r + 1.3 = 1.513274595 Simplifying r + 1.3 = 1.513274595 Reorder the terms: 1.3 + r = 1.513274595 Solving 1.3 + r = 1.513274595 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1.3' to each side of the equation. 1.3 + -1.3 + r = 1.513274595 + -1.3 Combine like terms: 1.3 + -1.3 = 0.0 0.0 + r = 1.513274595 + -1.3 r = 1.513274595 + -1.3 Combine like terms: 1.513274595 + -1.3 = 0.213274595 r = 0.213274595 Simplifying r = 0.213274595

Subproblem 2

r + 1.3 = -1.513274595 Simplifying r + 1.3 = -1.513274595 Reorder the terms: 1.3 + r = -1.513274595 Solving 1.3 + r = -1.513274595 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1.3' to each side of the equation. 1.3 + -1.3 + r = -1.513274595 + -1.3 Combine like terms: 1.3 + -1.3 = 0.0 0.0 + r = -1.513274595 + -1.3 r = -1.513274595 + -1.3 Combine like terms: -1.513274595 + -1.3 = -2.813274595 r = -2.813274595 Simplifying r = -2.813274595

Solution

The solution to the problem is based on the solutions from the subproblems. r = {0.213274595, -2.813274595}

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