# POLQ 2 | Lesson 4 | Try This! (Deriving the Quadratic Formula)

The standard form of the quadratic equation is $$ax^2+bx+c=0$$. Use your understanding of completing the square to put the steps below in the correct order to derive the quadratic formula.

 $$\left( x + \Large \frac{b}{2a} \right) = \pm \Large \sqrt{ \Large\frac{b^2-4ac}{4a^2}}$$ $$x^2 + \Large \frac{b}{a} \normalsize x + \left( \Large \frac{b}{2a} \right)^2 = \ – \Large \frac{c}{a} \normalsize + \left( \Large \frac{b}{2a} \right)^2$$ $$\Large \sqrt {\normalsize \left( x + \Large \frac{b}{2a} \right)^2} \normalsize = \pm \large \sqrt{ \Large \frac{b^2-4ac}{4a^2}}$$ $$x = \Large \frac {-b \pm \sqrt{b^2-4ac} } {2a}$$ $$\left( x + \Large \frac{b}{2a} \right)^2 = -\Large \frac{c}{a} \normalsize \cdot \Large \frac{4a}{4a} \normalsize + \Large \frac{b^2}{4a^2}$$ $$x + \Large \frac{b}{2a} \normalsize = \pm \Large \sqrt{ \Large \frac{b^2-4ac}{2a}}$$ $$x^2 + \Large \frac{b}{a} \normalsize x + \Large \frac{c}{a} \normalsize = 0$$,  $$a \neq 0$$ $$x = -\Large \frac{b}{2a} \normalsize \pm \Large \sqrt{ \Large \frac{b^2-4ac}{2a}}$$ $$\left( x + \Large \frac{b}{2a} \right)^2 = -\Large \frac{c}{a} \normalsize + \left( \Large \frac{b}{2a} \right)^2$$ $$x + \Large \frac{b}{2a} \normalsize = \pm \Large \frac{\sqrt{b^2-4ac}}{ \sqrt{4a^2}}$$ $$\left( x + \Large \frac{b}{2a} \right)^2 = -\Large \frac{c}{a} \normalsize + \Large \frac{b^2}{4a^2}$$ $$x^2 + \Large \frac{b}{a} \normalsize x = \ – \Large \frac{c}{a}$$ $$\left( x + \Large \frac{b}{2a} \right)^2 = \Large \frac{b^2-4ac}{4a^2}$$