Solving equations by taking square roots

Question

I am confused with solving equations by taking square roots. I have a math problem below as an example of what I am confused with.

$12x^2-154=0$

So first I believe you are supposed to move the constant to one side so it would be

$12x^2=154 $

After that I believe we need to divide by $12$, however $154$ is not divisible by $12$ nor do any perfect squares fit. I am aware they both share the greatest common factor of $2$, however I am not sure what to do with that or if it is needed. I am not sure.

Answer 1

You can work with fractions, I assume? Of course, in this case, your solutions for $x$ cannot be of integers, as you have already noticed. However, you can always do: $$12x^2=154$$ $$x^2=\frac{77}{6}$$ $$x=\pm\sqrt\frac{77}{6}$$