r^2+9r=80

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Solution for r^2+9r=80 equation:


Simplifying
r2 + 9r = 80

Reorder the terms:
9r + r2 = 80

Solving
9r + r2 = 80

Solving for variable 'r'.

Reorder the terms:
-80 + 9r + r2 = 80 + -80

Combine like terms: 80 + -80 = 0
-80 + 9r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '80' to each side of the equation.
-80 + 9r + 80 + r2 = 0 + 80

Reorder the terms:
-80 + 80 + 9r + r2 = 0 + 80

Combine like terms: -80 + 80 = 0
0 + 9r + r2 = 0 + 80
9r + r2 = 0 + 80

Combine like terms: 0 + 80 = 80
9r + r2 = 80

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 = 80 + 20.25

Reorder the terms:
20.25 + 9r + r2 = 80 + 20.25

Combine like terms: 80 + 20.25 = 100.25
20.25 + 9r + r2 = 100.25

Factor a perfect square on the left side:
(r + 4.5)(r + 4.5) = 100.25

Calculate the square root of the right side: 10.012492197

Break this problem into two subproblems by setting 
(r + 4.5) equal to 10.012492197 and -10.012492197.

Subproblem 1

r + 4.5 = 10.012492197 Simplifying r + 4.5 = 10.012492197 Reorder the terms: 4.5 + r = 10.012492197 Solving 4.5 + r = 10.012492197 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 = 10.012492197 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + r = 10.012492197 + -4.5 r = 10.012492197 + -4.5 Combine like terms: 10.012492197 + -4.5 = 5.512492197 r = 5.512492197 Simplifying r = 5.512492197

Subproblem 2

r + 4.5 = -10.012492197 Simplifying r + 4.5 = -10.012492197 Reorder the terms: 4.5 + r = -10.012492197 Solving 4.5 + r = -10.012492197 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 = -10.012492197 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + r = -10.012492197 + -4.5 r = -10.012492197 + -4.5 Combine like terms: -10.012492197 + -4.5 = -14.512492197 r = -14.512492197 Simplifying r = -14.512492197

Solution

The solution to the problem is based on the solutions from the subproblems. r = {5.512492197, -14.512492197}

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