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Solve for $z$ in $4z^2-81=0\text{.}$

Enter multiple answers in the form z=1 or z=-1. If you need to use the square root symbol, as in $\sqrt{17}\text{,}$ type it as sqrt(17).

Solution

Before we use the square root property we need to isolate the squared quantity.

$\begin{aligned} 4z^2-81\amp=0\\ 4z^2\amp=81\\ z^2\amp=\frac{81}{4} \end{aligned}$

$\begin{aligned} z\amp=-\sqrt{\frac{81}{4}} \amp\text{ or }\amp\amp z\amp=\sqrt{\frac{81}{4}}\\ z\amp=-\frac{9}{2}\amp\text{ or }\amp\amp z\amp=\frac{9}{2} \end{aligned}$

The solution set is $\left\{-\frac{9}{2},\frac{9}{2}\right\}\text{.}$