Chapter 8 - Section 8.4 - Equations Quadratic in Form - Exercise Set - Page 635: 5

{$ \pm 2i,\pm \sqrt 2$}

Since, $u^2+2u=8$ or, $u^2+2u-8=0$ Factorize the expression as follows: $(u+4)(u-2)=0$ or, $u=${$-4,2$} Replace $u$ with $x^2$, we have $x^2=-4 \implies x=\pm \sqrt {-4}$ or, $x=\pm 2i$ and $x^2=2$ This implies that $x= \pm 2i,\pm \sqrt 2$ Hence, our solution set is $x=${$ \pm 2i,\pm \sqrt 2$}