To rewrite the equation in standard form by completing the square, follow these steps:
- Move the constant term to the other side.
- Complete the square for the x-terms.
- Complete the square for the y-terms.
- Rewrite the equation with the squared terms factored.
- The equation in standard form after completing the square is: (x-1)² + (y-3)² = 25.
- Move the constant term to the other side of the equation: x^2 - 2x + y^2 - 6y = 15
- Complete the square for the x-terms by adding and subtracting (2 - 2)^2 = 1: x^2 - 2x + 1 + y^2 - 6y = 15 + 1
- Complete the square for the y-terms by adding and subtracting (2 - 6)^2 = 9: x^2 - 2x + 1 + y^2 - 6y + 9 = 15 + 1 + 9
- Rewrite the equation with the squared terms factored: (x - 1)^2 + (y - 3)^2 = 25
Therefore, the equation in standard form after completing the square is: (x - 1)^2 + (y - 3)^2 = 25
