Proving the quadratic formula (for dummies) I have looked at this question, and also at this one, but I don't understand how the quadratic formula can change from $ax^2+bx+c=0$ to $x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}$. I am not particularly good at maths, so can someone prove the quadratic formula in a simple way, with no complicated words? All help appreciated.

Look at each step here:
$$
\begin{align*}
a x^2 + b x + c
  &= 0 \\
a \left( x^2 +  \frac{b}{a} x \right) + c
  &= 0 \\
a \left( x^2 + \frac{b}{a} x + \frac{b^2}{4 a^2} \right) - \frac{b^2}{4 a} + c
  &= 0 \\
a \left( x + \frac{b}{2 a} \right)^2 
  &= \frac{b^2}{4 a} - c \\
\left( x + \frac{b}{2 a} \right)^2
  &= \frac{b^2 - 4 a c}{4 a^2} \\
x + \frac{b}{2 a}
  &= \frac{\pm\sqrt{b^2 - 4 a c}}{2 a} \\
x &= \frac{-b \pm\sqrt{b^2 - 4 a c}}{2 a}
\end{align*}
$$
