Chapter 4, Problem 39SGR

To determine

To find: The solution of given equation

Answer to Problem 39SGR

The solution of given equation is $x=\pm i\sqrt{2}$ .

Explanation of Solution

Given information:

The given equation.

  $4x^2+1=0$

Calculation:

Subtract 1 from each side after simplify divide by 4 both side

  $\begin{array}{l}4x^2+1-1=0-1\\ 4x^2=-1\\ \frac{4x^2}{4}=\frac{-1}{4}\\ x^2=-\frac{1}{4}\\ \sqrt{x^2}=\pm \sqrt{-\frac{1}{4}}\\ \sqrt{x^2}=\pm \sqrt{-1{\left(\frac{1}{2}\right)}^2}\\ x=\pm \frac{1}{2}i\end{array}$