Question

The surface area of the box of cereal displayed is 2x^2+48x+88. What is the value of x if the box of cereal has a total surface area of 192 in

Answer 1

Answer:

$x_2= \frac{-24 +28}{2}=2$

And the correct solution would be x=2 since a negative value not have a practica interpretation on this case.

Step-by-step explanation:

For this case the surface area is given by this formula:

$S (x) =2x^2 +48 x +88$   (1)

For this case we have that the total surface area is 192, so we need to set up equal to 192 and solve for the value of x like this:

$192= 2x^2 +48 x+88$

We can set up the last equuation equal to 0 like this:

$2x^2 +48 x-104 =0$

We can divide both sides of the equation by 2 and we got:

$x^2 +24x -52=0$

Now we can use the quadratic formula in order to solve the value of x given by:

$x = \frac{-b \pm \sqrt{b^2 -4ac}}{2a}$

For our equation a = 1, b = 24 and c = -52 and if we replace we got:

$x = \frac{-24 \pm \sqrt{(24)^2 -4(1)(-52)}}{2(1)}$

And the two solutions are:

$x_1 = \frac{-24 -28}{2}=-26$

$x_2= \frac{-24 +28}{2}=2$

And the correct solution would be x=2 since a negative value not have a practica interpretation on this case.