Question

Clara writes the equation (x – 13)(x + 8) = 196 to solve for the missing side length of a rectangle represented by the factor x + 8. What is the missing side length represented by x + 8 units of the rectangle?

7
15
20
28

Answer 1

(x − 13)(x + 8) = 196
x^2 − 5x − 104 = 196
x^2 − 5x − 300 = 0
Discriminant = 25 + 1200 = 1225 = 35^2
x = (5 ± 35)/2 → x = 20 or x = −15

x + 8 = 20 + 8 = 28 (−15 + 8 = −7 is not a valid side length), so the missing side is 28.