5r^2+20r-61=0

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Solution for 5r^2+20r-61=0 equation:


Simplifying
5r2 + 20r + -61 = 0

Reorder the terms:
-61 + 20r + 5r2 = 0

Solving
-61 + 20r + 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'.
-12.2 + 4r + r2 = 0

Move the constant term to the right:

Add '12.2' to each side of the equation.
-12.2 + 4r + 12.2 + r2 = 0 + 12.2

Reorder the terms:
-12.2 + 12.2 + 4r + r2 = 0 + 12.2

Combine like terms: -12.2 + 12.2 = 0.0
0.0 + 4r + r2 = 0 + 12.2
4r + r2 = 0 + 12.2

Combine like terms: 0 + 12.2 = 12.2
4r + r2 = 12.2

The r term is 4r.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4r + 4 + r2 = 12.2 + 4

Reorder the terms:
4 + 4r + r2 = 12.2 + 4

Combine like terms: 12.2 + 4 = 16.2
4 + 4r + r2 = 16.2

Factor a perfect square on the left side:
(r + 2)(r + 2) = 16.2

Calculate the square root of the right side: 4.02492236

Break this problem into two subproblems by setting 
(r + 2) equal to 4.02492236 and -4.02492236.

Subproblem 1

r + 2 = 4.02492236 Simplifying r + 2 = 4.02492236 Reorder the terms: 2 + r = 4.02492236 Solving 2 + r = 4.02492236 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + r = 4.02492236 + -2 Combine like terms: 2 + -2 = 0 0 + r = 4.02492236 + -2 r = 4.02492236 + -2 Combine like terms: 4.02492236 + -2 = 2.02492236 r = 2.02492236 Simplifying r = 2.02492236

Subproblem 2

r + 2 = -4.02492236 Simplifying r + 2 = -4.02492236 Reorder the terms: 2 + r = -4.02492236 Solving 2 + r = -4.02492236 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + r = -4.02492236 + -2 Combine like terms: 2 + -2 = 0 0 + r = -4.02492236 + -2 r = -4.02492236 + -2 Combine like terms: -4.02492236 + -2 = -6.02492236 r = -6.02492236 Simplifying r = -6.02492236

Solution

The solution to the problem is based on the solutions from the subproblems. r = {2.02492236, -6.02492236}

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