Question

1. $4x^{2}+1=0$

Explanation:

Step1: Isolate the $x^2$ term

$4x^2 = -1$

Step2: Solve for $x^2$

$x^2 = -\frac{1}{4}$

Step3: Take square root of both sides

$x = \pm\sqrt{-\frac{1}{4}} = \pm\frac{1}{2}i$

Answer:

$x = \frac{1}{2}i$ and $x = -\frac{1}{2}i$