SOLUTION: Find the center and radius by completing the square. x^2+y^2+10x+7=0

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Question 138443: Find the center and radius by completing the square.
x^2+y^2+10x+7=0
Found 2 solutions by solver91311, stanbon:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
Step 1: Move the constant term to the left side:

x%5E2%2By%5E2%2B10x=-7

Step 2: Put the x terms together and the y terms together:

x%5E2%2B10x%2By%5E2=-7

Step 3: Complete the square on the x variable. Divide the coefficient of the 1st degree x term by 2 and square the result: %2810%2F2%29%5E2=5%5E2=25. Add this value to both sides of the equation.

x%5E2%2B10x%2B25%2By%5E2=-7%2B25
x%5E2%2B10x%2B25%2By%5E2=18

Step 4: Complete the square on the y variable: Since there is no 1st degree y term, there is nothing to do.

Step 5: Factor the perfect squares:

%28x%2B5%29%5E2%2By%5E2=18, but re-write it thus so that the coordinates of the center are obvious:

%28x%2B5%29%5E2%2B%28y-0%29%5E2=18

Since we know that the equation of a circle with center at (h,k) and radius r is:

%28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2 we can see that the center of your circle is at (-5,0) and the radius is sqrt%2818%29=3sqrt%282%29

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Find the center and radius by completing the square.
x^2+y^2+10x+7=0
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Complete the square on the x-terms and the y-terms separately.
x^2 + 10x + 25 + y^2 = -7+25
(x+5)^2 + (y-0)^2 = 18
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Center at (-5,0)
radius = sqrt(18) = 3sqrt(2)
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Cheers,
Stan H.