SOLUTION: List all values of x satisfying the given condition. y1=(x+3), y2=(x-2), and y1y2=2

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Question 702320: List all values of x satisfying the given condition.
y1=(x+3), y2=(x-2), and y1y2=2
Answer by tommyt3rd(5050) About Me  (Show Source):
You can put this solution on YOUR website!
y1y2=2
(x+3)(x-2)=2
x^2+x-8=0

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B1x%2B-8+=+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=%281%29%5E2-4%2A1%2A-8=33.

Discriminant d=33 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-1%2B-sqrt%28+33+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%281%29%2Bsqrt%28+33+%29%29%2F2%5C1+=+2.37228132326901
x%5B2%5D+=+%28-%281%29-sqrt%28+33+%29%29%2F2%5C1+=+-3.37228132326901

Quadratic expression 1x%5E2%2B1x%2B-8 can be factored:
1x%5E2%2B1x%2B-8+=+1%28x-2.37228132326901%29%2A%28x--3.37228132326901%29
Again, the answer is: 2.37228132326901, -3.37228132326901. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B1%2Ax%2B-8+%29