Write the equation in standard form for the circle x^2+y^2+6x–1= 0.

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Identify equation and need: Identify the given equation and the need to complete the square for the x-terms. The given equation is x^2 + y^2 + 6x – 1 = 0. To write the equation in standard form, we need to complete the square for the x-terms.Group x-terms and leave space: Group the x-terms together and leave a space to complete the square. x^2 + 6x + ( ) + y^2 = 1 We have moved the constant term to the other side by adding 1 to both sides.Find number to complete square: Find the number to complete the square for the x-terms. To complete the square, we take half of the coefficient of x, which is 6/2 = 3, and square it, giving us 3^2 = 9.Add and subtract inside parentheses: Add and subtract the number found in Step 3 inside the parentheses. x^2 + 6x + 9 - 9 + y^2 = 1 We added 9 to complete the square and then subtracted 9 to keep the equation balanced.Rewrite equation with completed square: Rewrite the equation with the completed square for the x-terms. (x + 3)^2 - 9 + y^2 = 1 We have now completed the square for the x-terms.Move constant term from completed square: Move the constant term from the completed square to the other side. (x + 3)^2 + y^2 = 1 + 9 We added 9 to both sides to isolate the completed square and y^2 on one side.Simplify right side of equation: Simplify the right side of the equation. (x + 3)^2 + y^2 = 10 We have combined the constants on the right side.Write final equation in standard form: Write the final equation in standard form. The standard form for the equation of a circle is (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center and r is the radius. Our equation is now in this form with h = -3, k = 0, and r^2 = 10.

Write the equation in standard form for the circle $x^2+y^2+6x-1= 0$ .

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Write the equation in standard form for the circle x2+y2+6x−1=0x^2+y^2+6x-1= 0x2+y2+6x−1=0.

Write the equation in standard form for the circle $x^2+y^2+6x-1= 0$ .