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Natalka [10]
3 years ago
5

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
Mathematics
1 answer:
marissa [1.9K]3 years ago
8 0

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.

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