1. **State the problem:** Solve the quadratic equation $$x^2 + 2x = 35$$ by completing the square. 2. **Recall the formula and rule:** To complete the square for an equation of the form $$x^2 + bx = c$$, add $$\left(\frac{b}{2}\right)^2$$ to both sides to form a perfect square trinomial on the left. 3. **Identify coefficients:** Here, $$b = 2$$. 4. **Calculate $$\left(\frac{b}{2}\right)^2$$:** $$\left(\frac{2}{2}\right)^2 = 1^2 = 1$$ 5. **Add 1 to both sides:** $$x^2 + 2x + 1 = 35 + 1$$ 6. **Simplify right side:** $$x^2 + 2x + 1 = 36$$ 7. **Write left side as a perfect square:** $$\left(x + 1\right)^2 = 36$$ 8. **Take the square root of both sides:** $$x + 1 = \pm \sqrt{36}$$ 9. **Simplify the square root:** $$x + 1 = \pm 6$$ 10. **Solve for $$x$$:** - For $$x + 1 = 6$$, subtract 1: $$x = 6 - 1 = 5$$ - For $$x + 1 = -6$$, subtract 1: $$x = -6 - 1 = -7$$ **Final answer:** $$x = 5$$ or $$x = -7$$