r^2-r-36=0

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


Simplifying
r2 + -1r + -36 = 0

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

Solving
-36 + -1r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + -1r + 36 + r2 = 0 + 36

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

Combine like terms: -36 + 36 = 0
0 + -1r + r2 = 0 + 36
-1r + r2 = 0 + 36

Combine like terms: 0 + 36 = 36
-1r + r2 = 36

The r term is -1r.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1r + 0.25 + r2 = 36 + 0.25

Reorder the terms:
0.25 + -1r + r2 = 36 + 0.25

Combine like terms: 36 + 0.25 = 36.25
0.25 + -1r + r2 = 36.25

Factor a perfect square on the left side:
(r + -0.5)(r + -0.5) = 36.25

Calculate the square root of the right side: 6.020797289

Break this problem into two subproblems by setting 
(r + -0.5) equal to 6.020797289 and -6.020797289.


Subproblem 1
r + -0.5 = 6.020797289

Simplifying
r + -0.5 = 6.020797289

Reorder the terms:
-0.5 + r = 6.020797289

Solving
-0.5 + r = 6.020797289

Solving for variable 'r'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + r = 6.020797289 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + r = 6.020797289 + 0.5
r = 6.020797289 + 0.5

Combine like terms: 6.020797289 + 0.5 = 6.520797289
r = 6.520797289

Simplifying
r = 6.520797289


Subproblem 2
r + -0.5 = -6.020797289

Simplifying
r + -0.5 = -6.020797289

Reorder the terms:
-0.5 + r = -6.020797289

Solving
-0.5 + r = -6.020797289

Solving for variable 'r'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + r = -6.020797289 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + r = -6.020797289 + 0.5
r = -6.020797289 + 0.5

Combine like terms: -6.020797289 + 0.5 = -5.520797289
r = -5.520797289

Simplifying
r = -5.520797289


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {6.520797289, -5.520797289}

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