<s>[INST] Derivation of the quadratic equation So everyone knows that when $ax^2+bx+c=0$,$$x = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}.$$
But why does it equal this? I learned this in maths not 2 weeks ago and it makes no sense to me
 [/INST] $ax^2+bx+c=0　(a\neq0)$
$x^2+\frac{b}{a}x+\frac{c}{a}=0$
$x^2+\frac{b}{a}x=-\frac{c}{a}$
$x^2+\frac{b}{a}x+\frac{b^2}{4a^2}=-\frac{c}{a}+\frac{b^2}{4a^2}$
$(x+\frac{b}{2a})^2=\frac{b^2-4ac}{4a^2}$
$(x+\frac{b}{2a})=\pm\frac{\sqrt{b^2-4ac}}{\sqrt{4a^2}}$
$\therefore x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
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