<!-- date: 2010-09-05 -->
<!-- title: Lost Solutions -->
<!-- tag: Mathematics -->
<!-- key: yzmto -->
<!-- import: math.inc -->
<h2 id="algebraic-equation">Algebraic Equation</h2>
<p>
  Let me start this post with a simple equation:

  \[
    x(x - 2) = 3x.
  \]

  Let us first solve it in a <em>flawed</em> manner.  Dividing both
  sides by \( x \) we get

  \[
    x - 2 = 3.
  \]

  Adding \( 2 \) to both sides we get

  \[
    x = 5.
  \]

  Indeed, \( x = 5 \) is a solution of this equation.  If we
  su