r^2-33r+45=0

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Solution for r^2-33r+45=0 equation:


Simplifying
r2 + -33r + 45 = 0

Reorder the terms:
45 + -33r + r2 = 0

Solving
45 + -33r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '-45' to each side of the equation.
45 + -33r + -45 + r2 = 0 + -45

Reorder the terms:
45 + -45 + -33r + r2 = 0 + -45

Combine like terms: 45 + -45 = 0
0 + -33r + r2 = 0 + -45
-33r + r2 = 0 + -45

Combine like terms: 0 + -45 = -45
-33r + r2 = -45

The r term is -33r.  Take half its coefficient (-16.5).
Square it (272.25) and add it to both sides.

Add '272.25' to each side of the equation.
-33r + 272.25 + r2 = -45 + 272.25

Reorder the terms:
272.25 + -33r + r2 = -45 + 272.25

Combine like terms: -45 + 272.25 = 227.25
272.25 + -33r + r2 = 227.25

Factor a perfect square on the left side:
(r + -16.5)(r + -16.5) = 227.25

Calculate the square root of the right side: 15.074813432

Break this problem into two subproblems by setting 
(r + -16.5) equal to 15.074813432 and -15.074813432.


Subproblem 1
r + -16.5 = 15.074813432

Simplifying
r + -16.5 = 15.074813432

Reorder the terms:
-16.5 + r = 15.074813432

Solving
-16.5 + r = 15.074813432

Solving for variable 'r'.

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

Add '16.5' to each side of the equation.
-16.5 + 16.5 + r = 15.074813432 + 16.5

Combine like terms: -16.5 + 16.5 = 0.0
0.0 + r = 15.074813432 + 16.5
r = 15.074813432 + 16.5

Combine like terms: 15.074813432 + 16.5 = 31.574813432
r = 31.574813432

Simplifying
r = 31.574813432


Subproblem 2
r + -16.5 = -15.074813432

Simplifying
r + -16.5 = -15.074813432

Reorder the terms:
-16.5 + r = -15.074813432

Solving
-16.5 + r = -15.074813432

Solving for variable 'r'.

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

Add '16.5' to each side of the equation.
-16.5 + 16.5 + r = -15.074813432 + 16.5

Combine like terms: -16.5 + 16.5 = 0.0
0.0 + r = -15.074813432 + 16.5
r = -15.074813432 + 16.5

Combine like terms: -15.074813432 + 16.5 = 1.425186568
r = 1.425186568

Simplifying
r = 1.425186568


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {31.574813432, 1.425186568}

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