The quadratic equation which correctly models the situation is,
[tex]w^{2}-w-72=0[/tex]
Let us consider that width is w.
Given that The length of a rectangle is 2 less than twice its width.
[tex]length=2w-2[/tex]
Area of rectangle (A) [tex]=length *width[/tex]
The area is 144 squared centimeters.
[tex]w*(2w-2)=144\\\\2w^{2}-2w-144=0\\\\2(w^{2}-w-72 )=0 \\\\w^{2}-w-72 =0[/tex]
Hence, the quadratic equation which correctly models the situation is,
[tex]w^{2}-w-72=0[/tex]
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