Remember that
The volume of the box is given by
V=L*W*H
where
V=224 in3
L=(18-2x) in
W=(12-2x) in
H=x in
substitute in the formula
224=(18-2x)(12-2x)(x)
224=[(18)(12)-18(2x)-2x(12)+(2x)^2]x
224=[216-36x-24x+4x^2]x
224=[216-60x+4x^2]x
224=216x-60x^2+4x^3
4x^3-60x^2+216x-224=0
Solve the cubic equation by graphing
The values of x are
x=2
x=2.725
x=10.275 -----> is not a solution
Remember that
The domain for x is the interval
2x<12
x<6 in
interval (0,6)
Verify both values of x
For x=2 in
V=(18-2x)(12-2x)(x)
V=(18-2(2))(12-2(2))(2)
V=(14)(8)(2)=224 in3 -----> is ok
For x=2.725 in
V=(18-2(2.725))(12-2(2.725))(2.725)
V=(12.55)(6.55)(2.725)=224 in3
therefore
The answer is
The value of x can be x=2 in or x=2.725 in