A manufacturing company manufactures a cardboard box with a square base and a
height of 15 inches. Suppose the equation
2
x x 60 7,200 0
can be used to find the
length and width of the base of the box, each measuring x inches.
Use the zero product property to solve the equation. Show all the steps needed
to find both answers.
c. Explain how the solution relates to this situation.
Can somebody guide me step by step, I can't seem to get it or get the right answer
To solve the equation using the zero product property, we need to set each factor (x and x - 60) equal to zero and solve for x.
1. Start with the given equation: x^2 - 60x + 7,200 = 0.
2. Set x^2 - 60x + 7,200 = 0 equal to zero.
3. Now, we can factor the quadratic equation to solve for x:
(x - 120)(x - 60) = 0.
4. Set each factor equal to zero:
x - 120 = 0 and x - 60 = 0.
5. Solve for x in each equation:
For x - 120 = 0:
x = 120.
For x - 60 = 0:
x = 60.
So, the two solutions for x are x = 120 and x = 60.
c. The solutions x = 120 and x = 60 represent the possible lengths of the base of the cardboard box. Since the base of the box is a square, the length and width of the base should be the same. Therefore, the possible dimensions for the base of the box are 120 inches by 120 inches or 60 inches by 60 inches.
the equation is
x^2+60x-7,200=0