Question

Solve each of the following equations by using the method of completing the square:

$x^2+8x-2=0$

Answer 1

$$\begin{gathered} x^2+8x-2=0 \\ \Rightarrow x^2+8x=2 \\ \Rightarrow x^2+2\times x\times 4+4^2=2+4^2\left(\mathrm{Adding}{4}^2\mathrm{on}\mathrm{both}\mathrm{sides}\right) \\ \Rightarrow {\left(x+4\right)}^2=2+16=18 \end{gathered}$$
$$\begin{gathered} \Rightarrow x+4=\pm \sqrt{18}=\pm 3\sqrt{2}\left(\mathrm{Taking}\mathrm{square}\mathrm{root}\mathrm{on}\mathrm{both}\mathrm{sides}\right) \\ \Rightarrow x+4=3\sqrt{2}\mathrm{or}x+4=-3\sqrt{2} \\ \Rightarrow x=-4+3\sqrt{2}\mathrm{or}x=-4-3\sqrt{2} \end{gathered}$$
Hence, $\left(-4+3\sqrt{2}\right)$ and $\left(-4-3\sqrt{2}\right)$ are the roots of the given equation.