SOLUTION: If the volume of a box is 60ft^3, the width is 3ft, the height is 6 more than the length, what is the length? I have been trying this for HOURS.

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Question 944408: If the volume of a box is 60ft^3, the width is 3ft, the height is 6 more than the length, what is the length? I have been trying this for HOURS.
Found 2 solutions by Alan3354, macston:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Vol = L*W*H = 60
3*L*(L + 6) = 60
L*(L + 6) = 20
L^2 + 6L - 20 = 0
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Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B6x%2B-20+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%286%29%5E2-4%2A1%2A-20=116.

Discriminant d=116 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-6%2B-sqrt%28+116+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%286%29%2Bsqrt%28+116+%29%29%2F2%5C1+=+2.3851648071345
x%5B2%5D+=+%28-%286%29-sqrt%28+116+%29%29%2F2%5C1+=+-8.3851648071345

Quadratic expression 1x%5E2%2B6x%2B-20 can be factored:
1x%5E2%2B6x%2B-20+=+%28x-2.3851648071345%29%2A%28x--8.3851648071345%29
Again, the answer is: 2.3851648071345, -8.3851648071345. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B6%2Ax%2B-20+%29

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L =~ 2.385 ft

Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
V=L*W*H
60 cu ft=L*3*(L+6) Divide each side by 3 ft
20 sq ft=L*(L+6)
20+sq+ft=L%5E2%2B6L Subtract 20 sq ft from each side
0=L%5E2%2B6L-20+sq+ft
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation aL%5E2%2BbL%2Bc=0 (in our case 1L%5E2%2B6L%2B-20+=+0) has the following solutons:

L%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%286%29%5E2-4%2A1%2A-20=116.

Discriminant d=116 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-6%2B-sqrt%28+116+%29%29%2F2%5Ca.

L%5B1%5D+=+%28-%286%29%2Bsqrt%28+116+%29%29%2F2%5C1+=+2.3851648071345
L%5B2%5D+=+%28-%286%29-sqrt%28+116+%29%29%2F2%5C1+=+-8.3851648071345

Quadratic expression 1L%5E2%2B6L%2B-20 can be factored:
1L%5E2%2B6L%2B-20+=+1%28L-2.3851648071345%29%2A%28L--8.3851648071345%29
Again, the answer is: 2.3851648071345, -8.3851648071345. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B6%2Ax%2B-20+%29

Answers 2.385, -8.385 ANSWER L=2.385 (the other answer reverses L and H)
60 cu ft = (2.385 ft)(3 ft)H
60 cu ft=7.155H sq ft divide each side by 7.155 sq ft
8.386 ft=H
CHECK
60 cu ft=L*W*H
60 cu ft=(2.385 ft)(3 ft)(8.386 ft)
60 cu ft=60 cu ft