Chapter 8 - Sections 8.1-8.3 - Integrated Review - Summary on Solving Quadratic Equations - Page 504: 24

$x=\pm i\sqrt{11}$

Isolating the squared variable and then taking the square root of both sides, the solutions of the given quadratic equation, $ 5x^2+55=0 ,$ are \begin{array}{l}\require{cancel} 5x^2=-55 \\\\ x^2=-\dfrac{55}{5} \\\\ x^2=-11 \\\\ x=\pm\sqrt{-11} \\\\ x=\pm\sqrt{-1}\cdot\sqrt{11} \\\\ x=\pm i\sqrt{11} .\end{array}