To solve the quadratic equation r^2 + 2r - 6 = 0 by completing the square, follow these steps:
1. Move the constant term to the other side:
r^2 + 2r = 6
2. Take half of the coefficient of r, square it, and add it to both sides of the equation:
r^2 + 2r + 1 = 6 + 1
r^2 + 2r + 1 = 7
3. Factor the perfect square trinomial on the left side:
(r + 1)^2 = 7
4. Take the square root of both sides:
r + 1 = pm sqrt{7}
5. Solve for r:
r = -1 pm sqrt{7}
So, the solutions to the quadratic equation are r = -1 + sqrt{7} and r = -1 - sqrt{7} .
