1. **State the problem:** Solve the quadratic equation $$7r^2 - 14r = -7$$. 2. **Rewrite the equation:** Move all terms to one side to set the equation to zero: $$7r^2 - 14r + 7 = 0$$ 3. **Simplify the equation:** Divide every term by 7 to simplify: $$\cancel{7}r^2 - \cancel{7}2r + \cancel{7} = 0 \implies r^2 - 2r + 1 = 0$$ 4. **Recognize the quadratic form:** The equation is now: $$r^2 - 2r + 1 = 0$$ This is a perfect square trinomial. 5. **Factor the quadratic:** $$r^2 - 2r + 1 = (r - 1)^2 = 0$$ 6. **Solve for r:** Set the factor equal to zero: $$(r - 1)^2 = 0 \implies r - 1 = 0 \implies r = 1$$ **Final answer:** $$r = 1$$