SOLUTION: x2 + y2 = 9 x + y = 2

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Question 972799: x2 + y2 = 9
x + y = 2
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
x2 + y2 = 9
x + y = 2
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Use ^ (Shift 6) for exponents.
x^2 + y^2 = 9
x + y = 2 --> y = 2-x
Sub for y
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x^2 + (2-x)^2 = 9
2x^2 - 4x - 5 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B-4x%2B-5+=+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=%28-4%29%5E2-4%2A2%2A-5=56.

Discriminant d=56 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--4%2B-sqrt%28+56+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-4%29%2Bsqrt%28+56+%29%29%2F2%5C2+=+2.87082869338697
x%5B2%5D+=+%28-%28-4%29-sqrt%28+56+%29%29%2F2%5C2+=+-0.870828693386971

Quadratic expression 2x%5E2%2B-4x%2B-5 can be factored:
2x%5E2%2B-4x%2B-5+=+%28x-2.87082869338697%29%2A%28x--0.870828693386971%29
Again, the answer is: 2.87082869338697, -0.870828693386971. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-4%2Ax%2B-5+%29

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x = 1 - sqrt(14)/2
y = 2-x = 1 + sqrt(14)/2
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x = 1 + sqrt(14)/2
y = 2-x = 1 - sqrt(14)/2