How do you solve the equation $x^{2} - 16 x = - 20$ by completing the square?

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Solution

Find the equation $x^{2} - 16 x = - 20$ by completing the square:
Completing the square means the equation should be in $a x^{2} + b x + c$ :
$\begin{array}{rcl} x^{2} - 16 x & = & - 20 \\ \Rightarrow & x^{2} - 16 x + 8^{2} - 8^{2} = - 20 \\ \Rightarrow & {(x - 8)}^{2} - 64 = - 20 \\ \Rightarrow & {(x - 8)}^{2} = 44 \\ \Rightarrow & x - 8 = \pm \sqrt{44} \\ \Rightarrow & x = 8 \pm 2 \sqrt{11} \\ \Rightarrow & x = 8 \pm 2 \sqrt{11} \end{array}$
Hence, the equation after using the completing the square method is $\begin{array}{rcl} x & = & 8 \pm 2 \sqrt{11} \end{array}$ .

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