The length of a photograph is 1cm less than twice the width the area is 45cm² find the dimensions of the photograph.

Area=legnth times width

legnth is 1 less than 2 times width

l=legnth

w=width

l=-1+2w

l=2w-1

area=lw

area=45

subsitute

45=lw

45 = (2w-1) w

distribute

45=2w^2-w

subtract 45 from both sides

0=2w^2-w-45

factor because if we have xy=0 and we factor we can assume that x and/or y=0 so

trial and error factor

0 = (2w+9) (w-5)

set each to zero

0=2w+9

subtract 9

-9=2w

divide 2

-4.5=w

impossible since width cannot be negative so discard

w-5=0

add 5 to both sides

w=5

true

subsitute

l=2w-1

l=2 (5) - 1

l=10-1

l=9

w=5 cm

l=9 cm