# Chapter 1 - Section 1.4 - Quadratic Equations - 1.4 Exercises - Page 112: 34

$x=\left\{ 4-i\sqrt{5},4+ i\sqrt{5} \right\}$

#### Work Step by Step

Taking the square root of both sides, the solutions to the given equation, $(x-4)^2=-5 ,$ are \begin{array}{l}\require{cancel} x-4=\pm\sqrt{-5} \\\\ x-4=\pm\sqrt{-1}\cdot\sqrt{5} \\\\ x-4=\pm i\sqrt{5} \\\\ x=4\pm i\sqrt{5} .\end{array} Hence, the solutions are $x=\left\{ 4-i\sqrt{5},4+ i\sqrt{5} \right\} .$

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