User:Quantum Burrito/Quadratic Formula

$$\quad ax^2+bx+c=0$$

$$=> a\left[x^2+\frac{b}{a}x+\frac{c}{a}\right]=0$$

$$=> x^2+\frac{b}{a}x+\frac{c}{a}=0$$

$$=> \left(x+\frac{b}{2a}\right)^2-\frac{b^2}{(2a)^2}+\frac{c}{a}=0$$

$$=> \left(x+\frac{b}{2a}\right)^2-\frac{b^2}{4a^2}+\frac{4ac}{4a^2}=0$$

$$=> \left(x+\frac{b}{2a}\right)^2-\frac{b^2+4ac}{4a^2}=0$$

$$=> \left(x+\frac{b}{2a}\right)^2-\frac{b^2+4ac}{4a^2}=0$$

$$=> \left(x+\frac{b}{2a}\right)^2=\frac{b^2+4ac}{4a^2}$$

$$=> x+\frac{b}{2a}=\frac{\pm\sqrt{b^2+4ac}}{2a}$$

$$=> x=\frac{-b}{2a}+\frac{\pm\sqrt{b^2+4ac}}{2a}$$

$$=> x=\frac{-b\pm\sqrt{b^2+4ac}}{2a}$$