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Factorising a quadratic expression of the form $x^2+bx+c$ by completing the square.

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Write the following quadratic expression in the form $(x+a)^2+b$ by using the method of completing the square:

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\\[ \\simplify[unitFactor]{{a}x^2+{b}x+{c}} \\]

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For a quadratic expression of the form \\[ x^2+bx+c,\\] when written in completed square form it becomes \\[ \\left(x+\\frac{b}{2}\\right)^2 - \\left(\\frac{b}{2}\\right)^2+c.\\]

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So, \\[ \\begin{split} \\simplify[unitFactor]{{a}x^2+{b}x+{c}} &\\,=\\simplify[unitFactor]{(x+{b/2})^2 - {(b/2)}^2 + {c}}, \\\\ \\\\&\\,=\\simplify[unitFactor]{(x+{b/2})^2 +{c-(b/2)^2}}. \\end{split} \\]

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