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      <text>1.2.6 (General method - completing the square)</text>
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      <text><![CDATA[<h1>General method</h1>

<p>In order to solve a quadratic by completing the square we proceed using the following steps.</p>

<ol>
<li>Rearrange the given quadratic into standard form \(ax^2 + bx + c = 0\).</li>
<li>If \(a \not =1\) then divide all terms by \(a\).</li>
<li>Rearrange the equation so that only the constant term is on the right hand side. </li>
<li>Add \(\left(\frac{b}{2}\right)^2\) to both sides of the equation.</li>
<li>Factorise the left hand side (which should be a perfect square).</li>
<li>Take square roots of both sides (remembering both the positive and negative square roots).</li>
<li>Rearrange to get an equation of the form \(x = \dots\), the two values for \(x\) are then the solutions of the quadratic.</li>
<li>Check the values of \(x\) are indeed the roots by substituting them back into the quadratic and checking that this gives zero.</li>
</ol>]]></text>
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