The volume of a box is also the volume of a rectangular prism and can be found by using the following formula:

V = l * w * h

'V' - volume

'l' - length

'w' - width

'h' - height

We have

V = 560

h = 8

l = w + 3

w = ?

Replacing in the volume formula we have

560 = (w + 3) * w * 8

(w + 3) * w * 8 = 560 both sides divide by 8

w^2 + 3W = 70

w^3 + 3w - 70 = 0 (quadratic equation)

By using the formula for finding the solutions of quadratic equation we get

w1 = (-3 + ((3^3 - 4 *1*(-70))^(1/2)) / (2*1)

w1 = (-3 + (9 + 280) ^ (1/2)) / 2

w1 = (-3 + 289 ^ (1/2)) / 2

w1 = (-3 + 17)/2

w1 = 14 / 2

W1 = 7 in is one solution for the width

w2 = (-3 - ((3^3 - 4 *1*(-70))^(1/2)) / (2*1)

w2 = (-3 - (9 + 280) ^ (1/2)) / 2

w2 = (-3 - 289 ^ (1/2)) / 2

w2 = (-3 - 17)/2

w2 = - 20 / 2

w2 = -10 is not a solution since the width needs to be positive number and -10 < 0

Finally we can say that the width is 7 in and that is the only solution.