r^2-6r=2

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Solution for r^2-6r=2 equation: 


Simplifying
r2 + -6r = 2

Reorder the terms:
-6r + r2 = 2

Solving
-6r + r2 = 2

Solving for variable 'r'.

Reorder the terms:
-2 + -6r + r2 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + -6r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -6r + 2 + r2 = 0 + 2

Reorder the terms:
-2 + 2 + -6r + r2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -6r + r2 = 0 + 2
-6r + r2 = 0 + 2

Combine like terms: 0 + 2 = 2
-6r + r2 = 2

The r term is -6r.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6r + 9 + r2 = 2 + 9

Reorder the terms:
9 + -6r + r2 = 2 + 9

Combine like terms: 2 + 9 = 11
9 + -6r + r2 = 11

Factor a perfect square on the left side:
(r + -3)(r + -3) = 11

Calculate the square root of the right side: 3.31662479

Break this problem into two subproblems by setting 
(r + -3) equal to 3.31662479 and -3.31662479.


Subproblem 1
r + -3 = 3.31662479

Simplifying
r + -3 = 3.31662479

Reorder the terms:
-3 + r = 3.31662479

Solving
-3 + r = 3.31662479

Solving for variable 'r'.

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

Add '3' to each side of the equation.
-3 + 3 + r = 3.31662479 + 3

Combine like terms: -3 + 3 = 0
0 + r = 3.31662479 + 3
r = 3.31662479 + 3

Combine like terms: 3.31662479 + 3 = 6.31662479
r = 6.31662479

Simplifying
r = 6.31662479


Subproblem 2
r + -3 = -3.31662479

Simplifying
r + -3 = -3.31662479

Reorder the terms:
-3 + r = -3.31662479

Solving
-3 + r = -3.31662479

Solving for variable 'r'.

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

Add '3' to each side of the equation.
-3 + 3 + r = -3.31662479 + 3

Combine like terms: -3 + 3 = 0
0 + r = -3.31662479 + 3
r = -3.31662479 + 3

Combine like terms: -3.31662479 + 3 = -0.31662479
r = -0.31662479

Simplifying
r = -0.31662479


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {6.31662479, -0.31662479}

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