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

Answer: m^2-100=-99

Explanation:

Set up the binomial.

(m-10)

(m+10)

Multiply the binomial.

(m-10)(m+10)=-99

Apply difference of squares rule

(p+q)(p-q) = p2-q2

Answer: m^2-100=-99

Answer 2

`m {}^(2) - 100 = - 99`

Explanation:

Set up the binomial.

`(m - 10)`

`(m + 10)`

Multiply the binomial.

`(m - 10)(m + 10) = - 99`

Apply difference of squares rule

`(p + q)(p - q) = p {}^(2) - q {}^(2)`

`m {}^(2) - 100 = - 99`