SOLUTION: what is the volume of x if the volume of the box is 648 cubic feet, h=8 ft., L=x-7, W=x-7

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Question 823993: what is the volume of x if the volume of the box is 648 cubic feet, h=8 ft., L=x-7, W=x-7
Answer by algebrahouse.com(1659) About Me  (Show Source):
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Volume of a rectangular prism (or box) is:
V = lwh {length x width x height}

8(x - 7)(x - 7) = 648 {substituted given information into volume formula}
(x - 7)(x - 7) = 81 {divided each side by 8}
x² - 14x + 49 = 81 {used foil method to multiply binomials}
x² - 14x - 32 = 0 {subtracted 81 from each side}
(x - 16)(x + 2) = 0 {factored into two binomials}
x - 16 = 0 or x + 2 = 0 {set each factor equal to 0}
x = 16 or x = -2 {solved each equation for x}
x = 16 {x cannot be negative for x - 7 being the width and length}

the value of x is 16

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