Answer:
[tex]x_2= \frac{-24 +28}{2}=2[/tex]
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:
[tex]S (x) =2x^2 +48 x +88[/tex] (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:
[tex]192= 2x^2 +48 x+88[/tex]
We can set up the last equuation equal to 0 like this:
[tex]2x^2 +48 x-104 =0[/tex]
We can divide both sides of the equation by 2 and we got:
[tex] x^2 +24x -52=0[/tex]
Now we can use the quadratic formula in order to solve the value of x given by:
[tex]x = \frac{-b \pm \sqrt{b^2 -4ac}}{2a}[/tex]
For our equation a = 1, b = 24 and c = -52 and if we replace we got:
[tex]x = \frac{-24 \pm \sqrt{(24)^2 -4(1)(-52)}}{2(1)}[/tex]
And the two solutions are:
[tex]x_1 = \frac{-24 -28}{2}=-26[/tex]
[tex]x_2= \frac{-24 +28}{2}=2[/tex]
And the correct solution would be x=2 since a negative value not have a practica interpretation on this case.
