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

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) (Show Source): You can put this solution on YOUR website!
Step 1: Move the constant term to the left side:

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

Step 3: Complete the square on the x variable. Divide the coefficient of the 1st degree x term by 2 and square the result: . Add this value to both sides of the equation.

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:

, but re-write it thus so that the coordinates of the center are obvious:

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

we can see that the center of your circle is at (-5,0) and the radius is
Answer by stanbon(75887) (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
------------------
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
---------------------------
Center at (-5,0)
radius = sqrt(18) = 3sqrt(2)
====================
Cheers,
Stan H.
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