Marina solved the quadratic equation $9x^2-18x-720=0$ by completing the square. In the process, she came up with the equivalent equation $$(x+r)^2 = s,$$where $r$ and $s$ are constants.

What is $s$?
Dividing both sides of the equation $9x^2-18x-720=0$ by $9$, we have $$x^2-2x-80 = 0.$$The square which agrees with $x^2-2x-80$ except for the constant term is $(x-1)^2$, which is equal to $x^2-2x+1$ and thus to $(x^2-2x-80)+81$.

Therefore, by adding $81$ to each side, Marina rewrote the equation $x^2-2x-80 = 0$ as $$(x-1)^2 = 81.$$We have $r=-1$ and $s=\boxed{81}$.
81
Level 5
Algebra
Problem: Marina solved the quadratic equation $9x^2-18x-720=0$ by completing the square. In the process, she came up with the equivalent equation $$(x+r)^2 = s,$$where $r$ and $s$ are constants.

What is $s$?
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To find the value of $s$, we first need to complete the square for the quadratic equation $9x^2 - 18x - 720 = 0$. 

1. Start by isolating the quadratic and linear terms: 
   $9x^2 - 18x = 720$.

2. Factor out the coefficient of $x^2$, which is 9:
   $9(x^2 - 2x) = 720$.

3. Divide both sides by 9 to simplify:
   $x^2 - 2x = 80$.

4. To complete the square, take half of the coefficient of $x$, which is -2, divide it by 2 to get -1, and then square it to get 1. 

5. Add and subtract this square inside the equation:
   $x^2 - 2x + 1 - 1 = 80$.

6. This can be rewritten as:
   $(x - 1)^2 - 1 = 80$.

7. Rearranging gives:
   $(x - 1)^2 = 81$.

From this, we identify that $r = -1$ and $s = 81$. Thus, the value of $s$ is $81$.<|END_OF_LATENT|> The final answer is $81$.