Question

The area of a rectangle is 65 ft2, and the length of the rectangle is 3 ft less than twice the width. Find the dimensions of the rectangle.

Answer 1

What I have so far:
65ft^2=w(2w-3)
65ft^2=2w^2-3w
2w^2-3w-65
and then you're supposed to factor into two binomials, but I cant seem to find any factors that multiply to equal 65 and add make -3

Answer 2

2w^2-3w-65 factors to (w+5)(2w-13)

Answer 3

but -13+5 doesnt equal -3, so how do you know?

Answer 4

the rule works a bit differently because we have (2w^2) instead of just w^2

we can prove my factoring is correct using FOIL

(w+5)(2w-13) = (2w)(w) - 13(w) + 10w - 65 = 2w^2 - 3w - 65

Answer 5

this video may be helpful https://www.youtube.com/watch?v=07g-l8OuGPo

Answer 6

ok thank you!