The area of a rectangular floor is described by the equation w(w-9)=252 where w is the width of the floor in meters. What is the width o the floor?

##(w-21)(w+12)##

Given: ##w(w-9)=252##

Multiply everything inside the brackets by ##w##

##=>w^2-9w=252##

Subtract 252 from both sides

##w^2-9w-252=0##

Factors of 252 that have a difference of 9 are 12 and 21 We need -9 so the larger if the two is negative.

##(w-21)(w+12) =w^2+12w-21w-252color(red)(" Works")##