How to solve quadratic equation?

Today, I learned how to use the Complete the Square method to solve quadratic equations and discovered that it leads to the formula.

$$\begin{aligned} ax^2 + bx + c = 0 &\Rightarrow \left(x\sqrt{a} + b \div 2 \div \sqrt{a}\right)^2 = (\frac{b}{2\sqrt{a}})^2 - c = \frac{b^2}{4\sqrt{a}} - c \\ &\Rightarrow \left(x\sqrt{a} + b \div 2 \div \sqrt{a}\right)^2 = \left(\frac{b^2}{4a}\right) - c \\ &\Rightarrow x\sqrt{a} + b \div (2\sqrt{a}) = \pm \sqrt{\frac{b^2}{4a} - c} \\ &\Rightarrow x\sqrt{a} \times \sqrt{4a} + b \div (2\sqrt{a}) \times \sqrt{4a} = \pm \sqrt{b^2 - 4ac} \\ &\Rightarrow 2ax + b = \pm \sqrt{b^2 - 4ac} \\ &\Rightarrow x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \end{aligned}$$