The equation is [tex]\displaystyle{ x^2= \frac{9}{16} [/tex]. We can rewrite the equation as:
[tex]\displaystyle{ x^2= (\frac{3}{4})^2[/tex].
Our next step here is to take the square root of both sides, remembering that [tex] \sqrt{x^2}=|x|[/tex].
Thus, we have [tex]\displaystyle{ |x|= \frac{3}{4}[/tex]. Our final step is solving the absolute value equation, which yields:
[tex]\displaystyle{ x= \frac{3}{4}[/tex] or [tex]\displaystyle{ x= -\frac{3}{4}[/tex].
Solution set: { [tex]-\frac{3}{4}, \frac{3}{4}[/tex] }
