#### Answer

$x=+\dfrac{7}{2}i,-\dfrac{7}{2}i$

#### Work Step by Step

iven: $4x^2+49=0$
This can be written as: $4x^2=-49$
or, $x^2=-\dfrac{-49}{4}$
Apply The Square Root Property. $x=\pm \sqrt{-\dfrac{49}{4}}$
or, $x=\pm\sqrt{-1} \sqrt{\dfrac{49}{4}}$
Since, $\sqrt {-1}=i$
Thus, $x=\pm \dfrac{7}{2}i$
Hence, $x=+\dfrac{7}{2}i,-\dfrac{7}{2}i$