Question

The area of a rectangle can be expressed by

2x^2 - 7x - 4

If the rectangle has an area of 45, find the positive value for x

Answer 1

2x^2-7x-4=45
2x^2-7x=45+4
2x^2-7x=49
2x(x - 7) + 7(x - 7) = 0 ← factor out (x - 7)
(x - 7)(2x + 7) = 0

equate each factor to zero and solve for x
x - 7 = 0 ⇒ x = 7