Factoring Quadratics

Question

A rectangle has dimensions X +2 and X -7 where X is in centimetres if the area of the rectangle is 36 cm² what is the value of X

Answer 1

(X - 7)( X + 2) = 36

(X - 7)( X + 2) - 36 = 0

X² - 5x - 14 - 36 = 0

X² - 5x - 50 = 0

(X - 10)(X + 5) = 0

x = 10, - 5

x = 10

One side is X + 2 = 10 + 2 = 12. The other side equals 10 - 7 = 3.

3 times 12 = 36. We don't use the negative 5 because there's no such thing as a negative distance, so we use the factor ten instead.