Question: Fill in the blanks:
Play the game!
Find two numbers that multiply to make the 1st number and add to make the 2nd number.
Multiply -36; Add 0
______, and ______
1. **State the problem:** We need to find two numbers that multiply to $$-36$$ and add to $$0$$.
2. **Formula and rules:** Let the two numbers be $$x$$ and $$y$$.
We have:
$$x \times y = -36$$
$$x + y = 0$$
3. **Use the addition equation:** From $$x + y = 0$$, we get $$y = -x$$.
4. **Substitute into multiplication equation:**
$$x \times y = x \times (-x) = -x^2 = -36$$
5. **Solve for $$x$$:**
$$-x^2 = -36$$
Multiply both sides by $$-1$$:
$$\cancel{-}x^2 = \cancel{-}36$$
$$x^2 = 36$$
6. **Find $$x$$:**
$$x = \pm 6$$
7. **Find $$y$$:**
Since $$y = -x$$, if $$x = 6$$, then $$y = -6$$.
If $$x = -6$$, then $$y = 6$$.
8. **Answer:** The two numbers are $$6$$ and $$-6$$.
These numbers multiply to $$-36$$ and add to $$0$$.