SOLUTION: An apple orchard contains 84 trees. The number of trees per row is five more than the number of rows. Find the number of rows.

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Question 169636: An apple orchard contains 84 trees. The number of trees per row is five more than the number of rows. Find the number of rows.
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
let x be the number of rows and y be the number of trees in each row.
:
x*y=84...eq 1
x=y+5....eq 2
:
take x's value from eq 2 and plug it into eq 1
:
(y+5)y=84
:
y%5E2%2B5y-84=0
:
solve by quadratic formula y=7 and y =-12....throw out the negative value
:
using y's value in eq 2 we get:highlight%28x=7%2B5=12%29rows
:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ay%5E2%2Bby%2Bc=0 (in our case 1y%5E2%2B5y%2B-84+=+0) has the following solutons:

y%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=%285%29%5E2-4%2A1%2A-84=361.

Discriminant d=361 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-5%2B-sqrt%28+361+%29%29%2F2%5Ca.

y%5B1%5D+=+%28-%285%29%2Bsqrt%28+361+%29%29%2F2%5C1+=+7
y%5B2%5D+=+%28-%285%29-sqrt%28+361+%29%29%2F2%5C1+=+-12

Quadratic expression 1y%5E2%2B5y%2B-84 can be factored:
1y%5E2%2B5y%2B-84+=+1%28y-7%29%2A%28y--12%29
Again, the answer is: 7, -12. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B5%2Ax%2B-84+%29