r^2-9r+20.25=21.25

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Solution for r^2-9r+20.25=21.25 equation: 


Simplifying
r2 + -9r + 20.25 = 21.25

Reorder the terms:
20.25 + -9r + r2 = 21.25

Solving
20.25 + -9r + r2 = 21.25

Solving for variable 'r'.

Reorder the terms:
20.25 + -21.25 + -9r + r2 = 21.25 + -21.25

Combine like terms: 20.25 + -21.25 = -1
-1 + -9r + r2 = 21.25 + -21.25

Combine like terms: 21.25 + -21.25 = 0.00
-1 + -9r + r2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -9r + 1 + r2 = 0.00 + 1

Reorder the terms:
-1 + 1 + -9r + r2 = 0.00 + 1

Combine like terms: -1 + 1 = 0
0 + -9r + r2 = 0.00 + 1
-9r + r2 = 0.00 + 1

Combine like terms: 0.00 + 1 = 1
-9r + r2 = 1

The r term is -9r.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9r + 20.25 + r2 = 1 + 20.25

Reorder the terms:
20.25 + -9r + r2 = 1 + 20.25

Combine like terms: 1 + 20.25 = 21.25
20.25 + -9r + r2 = 21.25

Factor a perfect square on the left side:
(r + -4.5)(r + -4.5) = 21.25

Calculate the square root of the right side: 4.609772229

Break this problem into two subproblems by setting 
(r + -4.5) equal to 4.609772229 and -4.609772229.


Subproblem 1
r + -4.5 = 4.609772229

Simplifying
r + -4.5 = 4.609772229

Reorder the terms:
-4.5 + r = 4.609772229

Solving
-4.5 + r = 4.609772229

Solving for variable 'r'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + r = 4.609772229 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + r = 4.609772229 + 4.5
r = 4.609772229 + 4.5

Combine like terms: 4.609772229 + 4.5 = 9.109772229
r = 9.109772229

Simplifying
r = 9.109772229


Subproblem 2
r + -4.5 = -4.609772229

Simplifying
r + -4.5 = -4.609772229

Reorder the terms:
-4.5 + r = -4.609772229

Solving
-4.5 + r = -4.609772229

Solving for variable 'r'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + r = -4.609772229 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + r = -4.609772229 + 4.5
r = -4.609772229 + 4.5

Combine like terms: -4.609772229 + 4.5 = -0.109772229
r = -0.109772229

Simplifying
r = -0.109772229


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {9.109772229, -0.109772229}

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