r^2-12r+33=8

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Solution for r^2-12r+33=8 equation: 


Simplifying
r2 + -12r + 33 = 8

Reorder the terms:
33 + -12r + r2 = 8

Solving
33 + -12r + r2 = 8

Solving for variable 'r'.

Reorder the terms:
33 + -8 + -12r + r2 = 8 + -8

Combine like terms: 33 + -8 = 25
25 + -12r + r2 = 8 + -8

Combine like terms: 8 + -8 = 0
25 + -12r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-25' to each side of the equation.
25 + -12r + -25 + r2 = 0 + -25

Reorder the terms:
25 + -25 + -12r + r2 = 0 + -25

Combine like terms: 25 + -25 = 0
0 + -12r + r2 = 0 + -25
-12r + r2 = 0 + -25

Combine like terms: 0 + -25 = -25
-12r + r2 = -25

The r term is -12r.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12r + 36 + r2 = -25 + 36

Reorder the terms:
36 + -12r + r2 = -25 + 36

Combine like terms: -25 + 36 = 11
36 + -12r + r2 = 11

Factor a perfect square on the left side:
(r + -6)(r + -6) = 11

Calculate the square root of the right side: 3.31662479

Break this problem into two subproblems by setting 
(r + -6) equal to 3.31662479 and -3.31662479.


Subproblem 1
r + -6 = 3.31662479

Simplifying
r + -6 = 3.31662479

Reorder the terms:
-6 + r = 3.31662479

Solving
-6 + r = 3.31662479

Solving for variable 'r'.

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

Add '6' to each side of the equation.
-6 + 6 + r = 3.31662479 + 6

Combine like terms: -6 + 6 = 0
0 + r = 3.31662479 + 6
r = 3.31662479 + 6

Combine like terms: 3.31662479 + 6 = 9.31662479
r = 9.31662479

Simplifying
r = 9.31662479


Subproblem 2
r + -6 = -3.31662479

Simplifying
r + -6 = -3.31662479

Reorder the terms:
-6 + r = -3.31662479

Solving
-6 + r = -3.31662479

Solving for variable 'r'.

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

Add '6' to each side of the equation.
-6 + 6 + r = -3.31662479 + 6

Combine like terms: -6 + 6 = 0
0 + r = -3.31662479 + 6
r = -3.31662479 + 6

Combine like terms: -3.31662479 + 6 = 2.68337521
r = 2.68337521

Simplifying
r = 2.68337521


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {9.31662479, 2.68337521}

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