A new way to make quadratic equations easy (2019)
I briefly looked at the author&#x27;s paper. I find the account of the traditional method there questionable. He suggests it starts by going from:<p><pre><code>  x^2 + bx + c
</code></pre>
to<p><pre><code>  x^2 + bx + c + b^2&#x2F;4 - b^2&#x2F;4
</code></pre>
This step is freaking weird, I&#x27;ve never seen it before, and I don&#x27;t think this way. The process I follow is more like I observe that for general k:<p><pre><code>  (x + k)^2 = x^2 + 2kx + k^2
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so I observe that for k = b&#x2F;2 I get<p><pre><code>  (x + b&#x2F;2)^2 = x^2 + bx + b^2&#x2F;4
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and then I figure out what I need to add to both sides of that equation to make the RHS equal the original quadratic, which gives me:<p><pre><code>  (x + b&#x2F;2)^2 - b^2&#x2F;4 + c = x^2 + bx + c
</code></pre>
and I then find the roots of the RHS by instead finding them for the LHS. We say that the LHS is the result of &quot;completing the square&quot; on the RHS.<p>Question: Does anyone seriously learn to solve quadratics by rewriting <i>x^2 + bx + c</i> to <i>x^2 + bx + c + b^2&#x2F;4 - b^2&#x2F;4</i>. Because that seems like a bad way of learning it.