Solution :
Given a quadratic equation :
[tex]ax^2+bx+c = 0[/tex]
Step 1 : [tex]ax^2+bx+c = 0[/tex]
Step 2 : [tex]ax^2+bx=-c[/tex]
Step 3 : [tex]$x^2+\frac{b}{a}x = -\frac{c}{a}$[/tex]
Step 4 : [tex]$x^2+\left(\frac{b}{2a}\right)^2=\left(\frac{b}{2a}\right)^2\left(\frac{-c}{a}\right)$[/tex]
Step 5 : [tex]$\left(x+\frac{b}{2a}\right)^2=\left(\frac{b}{2a}\right)^2\left(\frac{-c}{a}\right)$[/tex]
Step 6 : [tex]$\left(x+\frac{b}{2a}\right)=\sqrt{\left(\frac{b}{2a}\right)^2\left(\frac{-c}{a}\right)$[/tex]
Step 7 : [tex]$x=\sqrt{\left(\frac{b}{2a}\right)^2\left(\frac{-c}{a}\right)} - \frac{b}{2a}$[/tex]
Step 8 : [tex]$x= \frac{-b \pm \sqrt{b^2-4ac}}{2a}$[/tex]
Thus the derivation for finding the roots of a quadratic equations.
