-r^2+13r+36=0

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Solution for -r^2+13r+36=0 equation:


Simplifying
-1r2 + 13r + 36 = 0

Reorder the terms:
36 + 13r + -1r2 = 0

Solving
36 + 13r + -1r2 = 0

Solving for variable 'r'.

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

Divide each side by '-1'.
-36 + -13r + r2 = 0

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + -13r + 36 + r2 = 0 + 36

Reorder the terms:
-36 + 36 + -13r + r2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + -13r + r2 = 0 + 36
-13r + r2 = 0 + 36

Combine like terms: 0 + 36 = 36
-13r + r2 = 36

The r term is -13r.  Take half its coefficient (-6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
-13r + 42.25 + r2 = 36 + 42.25

Reorder the terms:
42.25 + -13r + r2 = 36 + 42.25

Combine like terms: 36 + 42.25 = 78.25
42.25 + -13r + r2 = 78.25

Factor a perfect square on the left side:
(r + -6.5)(r + -6.5) = 78.25

Calculate the square root of the right side: 8.845903006

Break this problem into two subproblems by setting 
(r + -6.5) equal to 8.845903006 and -8.845903006.


Subproblem 1
r + -6.5 = 8.845903006

Simplifying
r + -6.5 = 8.845903006

Reorder the terms:
-6.5 + r = 8.845903006

Solving
-6.5 + r = 8.845903006

Solving for variable 'r'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + r = 8.845903006 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + r = 8.845903006 + 6.5
r = 8.845903006 + 6.5

Combine like terms: 8.845903006 + 6.5 = 15.345903006
r = 15.345903006

Simplifying
r = 15.345903006


Subproblem 2
r + -6.5 = -8.845903006

Simplifying
r + -6.5 = -8.845903006

Reorder the terms:
-6.5 + r = -8.845903006

Solving
-6.5 + r = -8.845903006

Solving for variable 'r'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + r = -8.845903006 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + r = -8.845903006 + 6.5
r = -8.845903006 + 6.5

Combine like terms: -8.845903006 + 6.5 = -2.345903006
r = -2.345903006

Simplifying
r = -2.345903006


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {15.345903006, -2.345903006}

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