Answer
$x=+ \dfrac{4}{5} i,- \dfrac{4}{5} i$
Work Step by Step
Given: $25x^2+16=0$
This can be written as: $25x^2=-16$
or, $x^2=-\dfrac{16}{25}$
Apply The Square Root Property. $x=\pm \sqrt{-\dfrac{16}{25}}$
or, $x=\pm \sqrt {-1} \sqrt{\dfrac{16}{25}}$
Since, $\sqrt {-1}=i$
Thus, $x=\pm \dfrac{4}{5}i$
Hence, $x=+ \dfrac{4}{5} i,- \dfrac{4}{5} i$
