1. We are asked to solve a quadratic equation by completing the square. 2. The general form of a quadratic equation is $ax^2 + bx + c = 0$. 3. To complete the square, we first move the constant term to the other side: $ax^2 + bx = -c$. 4. If $a \neq 1$, divide the entire equation by $a$ to make the coefficient of $x^2$ equal to 1: $$x^2 + \frac{b}{a}x = -\frac{c}{a}$$ 5. Next, add and subtract the square of half the coefficient of $x$ inside the equation to complete the square: $$x^2 + \frac{b}{a}x + \left(\frac{b}{2a}\right)^2 - \left(\frac{b}{2a}\right)^2 = -\frac{c}{a}$$ 6. Rewrite the left side as a perfect square and simplify the right side: $$\left(x + \frac{b}{2a}\right)^2 = -\frac{c}{a} + \left(\frac{b}{2a}\right)^2$$ 7. Simplify the right side: $$\left(x + \frac{b}{2a}\right)^2 = \frac{b^2 - 4ac}{4a^2}$$ 8. Take the square root of both sides: $$x + \frac{b}{2a} = \pm \frac{\sqrt{b^2 - 4ac}}{2a}$$ 9. Finally, solve for $x$: $$x = -\frac{b}{2a} \pm \frac{\sqrt{b^2 - 4ac}}{2a}$$ This is the quadratic formula derived by completing the square. If you provide a specific quadratic equation, I can solve it step-by-step using this method.