# A simpler form of the quadratic formula

In high school, I had to learn the famous quadratic formula by heart. It states that a quadratic polynomial $p$ defined as $p(x)=ax_{2}+bx+c$ has roots $x_{1,2}$ of the form $x_{1,2}=2a−b±b_{2}−4ac $

I think remembering formulae is a prime example of how math should not be taught. I think the proper way to solve quadratic equations is to complete the square:

First, rewrite the equation to the form $x_{2}+bx+c=0$

We can rewrite this as $(x−2b )_{2}−(2b )_{2}+c=0$

From there, it is easy to take it to $(x−2b )_{2}=(2b )_{2}−c$

and solve the resulting equation, remembering that $x_{2}=c$ has **two** solutions: $x=c $ and $x=−c $:

$x−2b =±(2b )_{2}−c $

So $x_{1,2}=2b ±(2b )_{2}−c $.

If you, for some reason, insist on learning a formula (for example, because it is easier or faster to apply), there is an alternative that I find to be preferable to the classical quadratic formula. By setting $a=−2pq $ and $b=−pr $, any quadratic equation of the form $px_{2}+qx+r=0$ can be reduced to the form $x_{2}=2ax+b$

which has the solution $x_{1,2}=a±a_{2}+b $

and is far more elegant, in my opinion.

In conclusion, I think it’s preferable to *not* teach the quadratic formula in high school, and instead teach how to complete the square. Not only does this relieve you of the burden of remembering a formula, it is also much more instructive and opens doors to more elaborate algebraic manipulation.