Question

Two numbers are 10 units away in different directions from their midpoint, m, on a number line. The product of the numbers is –99.

Which equation can be used to find m, the midpoint of the two numbers?

(m – 5)(m + 5) = 99
(m – 10)(m + 10) = 99
m2 – 25 = –99
m2 – 100 = –99

Answer 1

Let the numbers be m − 10 and m + 10. Their product is

(m − 10)(m + 10) = −99

Expanding gives m^2 − 100 = −99. So the correct equation is m^2 − 100 = −99.