Chapter I, Problem 19E

To determine

To find: The solution of the equation $4x^2+9=0$.

Answer to Problem 19E

The solutions of the equation $4x^2+9=0$ is $x=\pm \frac{3}{2}i$.

Explanation of Solution

Simplify the expression $4x^2+9=0$ as follows.

$\begin{array}{l}4x^2+9=0\\ 4x^2=-9\\ x^2=-\frac{9}{4}\\ x=\sqrt{-\frac{9}{4}}\end{array}$

Further simplified as,

$\begin{array}{l}x=\pm \sqrt{-\frac{9}{4}}\\ x=\pm \sqrt{\frac{9}{4}}i\\ x=\pm \frac{3}{2}i\end{array}$

Thus, the solutions of the equation $4x^2+9=0$ is $x=\pm \frac{3}{2}i$.