1. **State the problem:** Solve the quadratic equation $$x^2 + 6x - 7 = 0$$ using the method of completing the square. 2. **Rewrite the equation:** Move the constant term to the right side: $$x^2 + 6x = 7$$ 3. **Complete the square:** Take half of the coefficient of $x$, which is 6, divide by 2 to get 3, then square it to get $3^2 = 9$. Add 9 to both sides to keep the equation balanced: $$x^2 + 6x + 9 = 7 + 9$$ 4. **Simplify both sides:** $$x^2 + 6x + 9 = 16$$ 5. **Rewrite the left side as a perfect square:** $$ (x + 3)^2 = 16 $$ 6. **Take the square root of both sides:** $$ x + 3 = \pm 4 $$ 7. **Solve for $x$:** $$ x = -3 \pm 4 $$ This gives two solutions: $$ x = -3 + 4 = 1 $$ $$ x = -3 - 4 = -7 $$ **Final answer:** $$x = 1 \text{ or } x = -7$$