Question

Gary works at a bakery, and he needs to select a rectangular cookie sheet with an area of 192 square inches. The area of the cookie sheet is represented by the expression given below.
x² + 4x

Complete the given statements, and find the width of the cookie sheet.

Step 1: x² + 4x = 192
Step 2: x(x + ___ ) = 192 The length is x. The width is ___
Step 3: x² + 4x = 192 = 0
Step 4: (x + ___ ) (x - 12) = 0
Because the length can't be ___, the length is 12, and the width is ___

Here is the selection of values that can be inserted into the blank spaces. Note that not all of them will be used.
12
4
x
x + 4
-16
16
x + 12
x²

Answer 1

 
x-------> the length of a rectangular cookie sheet

we know that
area of a rectangular cookie sheet=length*width
area of a rectangular cookie sheet=192 in²
area of a rectangular cookie sheet=x² + 4x-----> x*(x+4)

Step 1: x² + 4x = 192
Step 2: x(x + 4 ) = 192 The length is x. The width is (x+4)
Step 3: x² + 4x = 192=0
we have 
x² + 4x = 192
x² + 4x - 192=0
using a graph tool-----> to resolve the second order equation
see the aattached figure
the solution is 
x=-16
x=12
(x+16)*(x-12)=0

the length is x=12 in
and the width is-----> (x+4)-----> 12+4----> 16 in

Step 4: (x +16) (x - 12) = 0
Because the length can't be -16  the length is 12, and the width is 16