### Instruction: What is the product of the solutions of the equation $-35=-x^2-2x?$.### Response: I recognize that this is a quadratic equation, so I can try to factor it or use the quadratic formula to find the solutions.
However, before I do that, I notice that I can simplify the equation by adding $x^2+2x$ to both sides.
This gives me $x^2+2x-35=0.$
Now I can try to factor this by looking for two numbers that multiply to -35 and add to 2.
I see that 7 and -5 work, so I can write $x^2+2x-35=(x+7)(x-5).$
Therefore, the solutions are $x=-7$ and $x=5.$
To find the product of the solutions, I just multiply them together: $(-7)(5)=-35.$