SOLUTION: X-2y=10 Y=x^2+2x-15

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Question 1190112: X-2y=10
Y=x^2+2x-15
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
X-2y=10
Y=x^2+2x-15
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2y = x-10
2y = 2x^2 + 4x - 30
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x-10 = 2x^2 + 4x - 30
2x^2 + 3x - 20 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B3x%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=%283%29%5E2-4%2A2%2A-20=169.

Discriminant d=169 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-3%2B-sqrt%28+169+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%283%29%2Bsqrt%28+169+%29%29%2F2%5C2+=+2.5
x%5B2%5D+=+%28-%283%29-sqrt%28+169+%29%29%2F2%5C2+=+-4

Quadratic expression 2x%5E2%2B3x%2B-20 can be factored:
2x%5E2%2B3x%2B-20+=+%28x-2.5%29%2A%28x--4%29
Again, the answer is: 2.5, -4. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B3%2Ax%2B-20+%29

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x = 2.5, y = -3.75
x = -4, y = -7