1. **State the problem:** Solve a quadratic equation using the square method (completing the square). 2. **General formula:** For a quadratic equation $ax^2 + bx + c = 0$, we can solve by completing the square using the formula: $$ax^2 + bx + c = 0 \implies x^2 + \frac{b}{a}x = -\frac{c}{a}$$ 3. **Steps to complete the square:** - Take half of the coefficient of $x$, which is $\frac{b}{2a}$. - Square it: $\left(\frac{b}{2a}\right)^2$. - Add and subtract this square inside the equation to form a perfect square trinomial. 4. **Rewrite the equation:** $$x^2 + \frac{b}{a}x + \left(\frac{b}{2a}\right)^2 = -\frac{c}{a} + \left(\frac{b}{2a}\right)^2$$ 5. **Express as a square:** $$\left(x + \frac{b}{2a}\right)^2 = -\frac{c}{a} + \frac{b^2}{4a^2}$$ 6. **Simplify the right side:** $$\left(x + \frac{b}{2a}\right)^2 = \frac{b^2 - 4ac}{4a^2}$$ 7. **Take the square root of both sides:** $$x + \frac{b}{2a} = \pm \frac{\sqrt{b^2 - 4ac}}{2a}$$ 8. **Isolate $x$:** $$x = -\frac{b}{2a} \pm \frac{\sqrt{b^2 - 4ac}}{2a}$$ 9. **Final solution:** $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ This is the quadratic formula derived by completing the square, which solves any quadratic equation. **Note:** The square method is useful to understand the origin of the quadratic formula and to solve quadratics when factoring is difficult.