r^2=20-9r

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Solution for r^2=20-9r equation:


Simplifying
r2 = 20 + -9r

Solving
r2 = 20 + -9r

Solving for variable 'r'.

Reorder the terms:
-20 + 9r + r2 = 20 + -9r + -20 + 9r

Reorder the terms:
-20 + 9r + r2 = 20 + -20 + -9r + 9r

Combine like terms: 20 + -20 = 0
-20 + 9r + r2 = 0 + -9r + 9r
-20 + 9r + r2 = -9r + 9r

Combine like terms: -9r + 9r = 0
-20 + 9r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + 9r + 20 + r2 = 0 + 20

Reorder the terms:
-20 + 20 + 9r + r2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + 9r + r2 = 0 + 20
9r + r2 = 0 + 20

Combine like terms: 0 + 20 = 20
9r + r2 = 20

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 = 20 + 20.25

Reorder the terms:
20.25 + 9r + r2 = 20 + 20.25

Combine like terms: 20 + 20.25 = 40.25
20.25 + 9r + r2 = 40.25

Factor a perfect square on the left side:
(r + 4.5)(r + 4.5) = 40.25

Calculate the square root of the right side: 6.34428877

Break this problem into two subproblems by setting 
(r + 4.5) equal to 6.34428877 and -6.34428877.

Subproblem 1

r + 4.5 = 6.34428877 Simplifying r + 4.5 = 6.34428877 Reorder the terms: 4.5 + r = 6.34428877 Solving 4.5 + r = 6.34428877 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 = 6.34428877 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + r = 6.34428877 + -4.5 r = 6.34428877 + -4.5 Combine like terms: 6.34428877 + -4.5 = 1.84428877 r = 1.84428877 Simplifying r = 1.84428877

Subproblem 2

r + 4.5 = -6.34428877 Simplifying r + 4.5 = -6.34428877 Reorder the terms: 4.5 + r = -6.34428877 Solving 4.5 + r = -6.34428877 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 = -6.34428877 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + r = -6.34428877 + -4.5 r = -6.34428877 + -4.5 Combine like terms: -6.34428877 + -4.5 = -10.84428877 r = -10.84428877 Simplifying r = -10.84428877

Solution

The solution to the problem is based on the solutions from the subproblems. r = {1.84428877, -10.84428877}

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