Answer
$t=\displaystyle \frac{\sqrt{11}}{2}$ or $t=-\displaystyle \frac{\sqrt{11}}{2}$
Work Step by Step
$ 4t^{2}=11\qquad$...divide both sides with $4$.
$ t^{2}=\displaystyle \frac{11}{4}\qquad$...use the principle of square roots:
For any real number $k$ , if $x^{2}=k$ , then
$x=\sqrt{k}$ or $x=-\sqrt{k}$
$ t=\pm\sqrt{\frac{11}{4}}\qquad$...apply the quotient rule of square roots:$\displaystyle \sqrt{\frac{a}{b}=}\frac{\sqrt{a}}{\sqrt{b}}$
$ t=\displaystyle \pm\frac{\sqrt{11}}{\sqrt{4}}\qquad$...simplify.
$ t=\displaystyle \pm\frac{\sqrt{11}}{2}\qquad$...the symbol $\pm$ indicates two solutions.
$t=\displaystyle \frac{\sqrt{11}}{2}$ or $t=-\displaystyle \frac{\sqrt{11}}{2}$
