I need help getting to the next step please I'm not asking for the answer just a guide to the next step?

Question

There is a rectagular metal with one side 30'' longer than wide. The are cutting square from the corners that are 6'' longe and the flaps are folded upward to form an open box. Volume of the box= 594 in(cubed). What are the original deminsions.

So this is what I have done thus far:

594=(x+30-12)(x-12)(2)

I divided the two

297=(x+18)(x-12)

297=x2+18x-12x-216

297=x2+6x-216

Subtracted 297

x2+6x-513=0

So now I'm thinking that I should factor, and the book examples tell me I must factor this problem out, but I cannot find any numbers that multiply to -513 to equal 6. So should I plug it into the quadratic formula from here?

Answer 1

Step 1 looks problematic:

Let x be original sheet width.

Length of box = x-12+30

width of the box = x-12

depth of the box = 6

(x+30-12)(x-12)(6)=594

(x+18)(x-12)=594/6=99

x^2+6x-216=99

x^2+6x-315=0

(x-15)(x+21)=0

occurs when x=15 or x=-21

only x=15 has meaning in this context.

Width =15

Length=width+30"=45"

box dimensions were 3 x 33 x 6 = 594 in^3

Answer 2

Yup Quadratic that puppy up... should get 19.84731932 and -25.84731932 but the neg doesn't make sense so u only use the first one. I didn't look over your math up till there though but if the last step u did is right that should be the answer, others feel free to correct me.

Answer 3

i would use the quadratic formula or graph it on your calculator and find the zeros