# Chapter 11 - Quadratic Functions and Equations - 11.1 Quadratic Equations - 11.1 Exercise Set - Page 706: 19

$d=\pm \dfrac{9}{2}i$

#### Work Step by Step

Since $x^2=a$ implies $x=\pm\sqrt{a}$ (the Square Root Principle), the solutions to the given equation, $4d^2+81=0 ,$ are \begin{array}{l}\require{cancel} 4d^2=-81 \\\\ d^2=\dfrac{-81}{4} \\\\ d=\pm\sqrt{\dfrac{-81}{4}} \\\\ d=\pm\sqrt{-1}\cdot\sqrt{\dfrac{81}{4}} \\\\ d=\pm i\cdot\sqrt{\left( \dfrac{9}{2} \right)^2} \\\\ d=\pm i\cdot\dfrac{9}{2} \\\\ d=\pm \dfrac{9}{2}i .\end{array}

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