SOLUTION: how do you solve (x^2\16)+ (y^2\16)=1 y=x+3

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Question 22588: how do you solve (x^2\16)+ (y^2\16)=1 y=x+3
Answer by stanbon!(97) About Me  (Show Source):
You can put this solution on YOUR website!
Multiply thru by 16 to get x^2+y^2 = 16
Substitute y=x+3 to get:
x^2 +x^2+6x+9=16
2x^2 + 6x -7 =0
Use the quadratic formula to get
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B6x%2B-7+=+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%2A2%2A-7=92.

Discriminant d=92 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-6%2B-sqrt%28+92+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%286%29%2Bsqrt%28+92+%29%29%2F2%5C2+=+0.89791576165636
x%5B2%5D+=+%28-%286%29-sqrt%28+92+%29%29%2F2%5C2+=+-3.89791576165636

Quadratic expression 2x%5E2%2B6x%2B-7 can be factored:
2x%5E2%2B6x%2B-7+=+2%28x-0.89791576165636%29%2A%28x--3.89791576165636%29
Again, the answer is: 0.89791576165636, -3.89791576165636. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B6%2Ax%2B-7+%29


Cheers,
Stan H.