SOLUTION: I keep trying to do the formula for volume, but this question is causing me a major headache, please help..'The volume of a rectangular prism with height 7 inches can be given by V

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Question 104901This question is from textbook Introductory & Intermediate Algebra
: I keep trying to do the formula for volume, but this question is causing me a major headache, please help..'The volume of a rectangular prism with height 7 inches can be given by V(x)= 63x + 42x^2, where x is its width. If the volume is 600 cubic inches, find the width to the nearest hundredth of an inch. Thank you for your help, if you can show me the steps better than this book, maybe I can figure them out better. This question is from textbook Introductory & Intermediate Algebra

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
You know the height is 7 inches and the volume is 600 cubic inches.
You also know that a formula for volume, V(x),is given by the function,
V%28x%29=63x+%2B+42x%5E2 where x is the width.
Solve for x when V(x)=600.
63x%2B42x%5E2=600
42x%5E2%2B63x-600=0 Move all terms to one side.
14x%5E2%2B21x-200=0 Divide both sides by 6.
Use the quadratic formulat to solve for x.
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
where a=14, b=21, and c=-200.
x+=+%28-21+%2B-+sqrt%28+21%5E2-4%2A14%2A%28-200%29+%29%29%2F%282%2A14%29+
x+=+%28-21+%2B-+sqrt%28+441%2B11200+%29%29%2F%2828%29+
x+=+%28-21+%2B-+sqrt%28+11641+%29%29%2F%2828%29+
sqrt%2811641%29=+%28107.89%29
x+=+%28-21+%2B-+%28107.89%29%29%2F%2828%29+
x=-4.6 and x=3.1
Since a negative width does not make sense, there is one solution.
x=3.1 inches.
The volume of a rectangular prism is also given by, V=LxWxH.
Since H=7 inches and W=3.1 inches, then
LWH=600
L%287%29%283.1%29=600
L=600%2F%287%2A3.1%29
L=27.6 inches