Write the equation in standard form for the circle x^2+y^2+10y–25= 0.

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Identify equation and need: Identify the given equation and the need to complete the square for y. The given equation is x^2 + y^2 + 10y – 25 = 0. To write the equation in standard form, we need to complete the square for the y terms.Group and leave space: Group the y terms and leave a space for completing the square. x^2 + (y^2 + 10y + __) - 25 = 0 We will add and subtract the same value inside the parentheses to complete the square.Calculate value for completion: Calculate the value needed to complete the square for y. To complete the square, we take half of the coefficient of y, which is 10/2 = 5, and square it, resulting in 5^2 = 25.Add and subtract calculated value: Add and subtract the calculated value inside the parentheses. x^2 + (y^2 + 10y + 25 - 25) - 25 = 0 Now we have the perfect square trinomial for y and an extra -25 that we will move outside the parentheses.Write perfect square trinomial: Write the perfect square trinomial and simplify the equation. x^2 + (y + 5)^2 - 25 - 25 = 0 Combine the constant terms on the right side.Simplify equation: Combine the constants and write the equation in standard form. x^2 + (y + 5)^2 - 50 = 0 Add 50 to both sides to get the standard form. x^2 + (y + 5)^2 = 50

Write the equation in standard form for the circle $x^2+y^2+10y-25= 0$ .

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Write the equation in standard form for the circle x2+y2+10y−25=0x^2+y^2+10y-25= 0x2+y2+10y−25=0.

Write the equation in standard form for the circle $x^2+y^2+10y-25= 0$ .