0=r^2+5r-113.1

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Solution for 0=r^2+5r-113.1 equation:


Simplifying
0 = r2 + 5r + -113.1

Reorder the terms:
0 = -113.1 + 5r + r2

Solving
0 = -113.1 + 5r + r2

Solving for variable 'r'.

Combine like terms: 0 + 113.1 = 113.1
113.1 + -5r + -1r2 = -113.1 + 5r + r2 + 113.1 + -5r + -1r2

Reorder the terms:
113.1 + -5r + -1r2 = -113.1 + 113.1 + 5r + -5r + r2 + -1r2

Combine like terms: -113.1 + 113.1 = 0.0
113.1 + -5r + -1r2 = 0.0 + 5r + -5r + r2 + -1r2
113.1 + -5r + -1r2 = 5r + -5r + r2 + -1r2

Combine like terms: 5r + -5r = 0
113.1 + -5r + -1r2 = 0 + r2 + -1r2
113.1 + -5r + -1r2 = r2 + -1r2

Combine like terms: r2 + -1r2 = 0
113.1 + -5r + -1r2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-113.1 + 5r + r2 = 0

Move the constant term to the right:

Add '113.1' to each side of the equation.
-113.1 + 5r + 113.1 + r2 = 0 + 113.1

Reorder the terms:
-113.1 + 113.1 + 5r + r2 = 0 + 113.1

Combine like terms: -113.1 + 113.1 = 0.0
0.0 + 5r + r2 = 0 + 113.1
5r + r2 = 0 + 113.1

Combine like terms: 0 + 113.1 = 113.1
5r + r2 = 113.1

The r term is 5r.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5r + 6.25 + r2 = 113.1 + 6.25

Reorder the terms:
6.25 + 5r + r2 = 113.1 + 6.25

Combine like terms: 113.1 + 6.25 = 119.35
6.25 + 5r + r2 = 119.35

Factor a perfect square on the left side:
(r + 2.5)(r + 2.5) = 119.35

Calculate the square root of the right side: 10.92474256

Break this problem into two subproblems by setting 
(r + 2.5) equal to 10.92474256 and -10.92474256.


Subproblem 1
r + 2.5 = 10.92474256

Simplifying
r + 2.5 = 10.92474256

Reorder the terms:
2.5 + r = 10.92474256

Solving
2.5 + r = 10.92474256

Solving for variable 'r'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + r = 10.92474256 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + r = 10.92474256 + -2.5
r = 10.92474256 + -2.5

Combine like terms: 10.92474256 + -2.5 = 8.42474256
r = 8.42474256

Simplifying
r = 8.42474256


Subproblem 2
r + 2.5 = -10.92474256

Simplifying
r + 2.5 = -10.92474256

Reorder the terms:
2.5 + r = -10.92474256

Solving
2.5 + r = -10.92474256

Solving for variable 'r'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + r = -10.92474256 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + r = -10.92474256 + -2.5
r = -10.92474256 + -2.5

Combine like terms: -10.92474256 + -2.5 = -13.42474256
r = -13.42474256

Simplifying
r = -13.42474256


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {8.42474256, -13.42474256}

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