SOLUTION: A number added to the product of 6 and the reciprocal of the number equals -5. Find the number.

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Question 412594: A number added to the product of 6 and the reciprocal of the number equals -5. Find the number.
Answer by jjordan95(63) About Me  (Show Source):
You can put this solution on YOUR website!
First turn this into an algebraic equation.
x%2B6%2A1%2Fx=-5 = x%2B6%2Fx=-5
Now, you can use the quadratic formula, multiply both sides by x, x%5E2%2B6=-5x
move everything to one side. x%5E2%2B5x%2B6=0 Now simply use the quadratic formula.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B5x%2B6+=+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=%285%29%5E2-4%2A1%2A6=1.

Discriminant d=1 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-5%2B-sqrt%28+1+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%285%29%2Bsqrt%28+1+%29%29%2F2%5C1+=+-2
x%5B2%5D+=+%28-%285%29-sqrt%28+1+%29%29%2F2%5C1+=+-3

Quadratic expression 1x%5E2%2B5x%2B6 can be factored:
1x%5E2%2B5x%2B6+=+1%28x--2%29%2A%28x--3%29
Again, the answer is: -2, -3. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B5%2Ax%2B6+%29