How to Isolate x in a Complex RLC Circuit Equation?

[p75213]

Can somebody point me in the right direction with this?

$$\begin{array}{l}<br /> \sqrt {{R^2} + {{\left( {xL - {\textstyle{1 \over {xC}}}} \right)}^2}} = \sqrt 2 R \\ <br /> {R^2} + {\left( {xL - {\textstyle{1 \over {xC}}}} \right)^2} = 2{R^2} \\ <br /> xL - {\textstyle{1 \over {xC}}} = R\sqrt {2 - 1} \\ <br /> \end{array}$$

 

[scurty]

I'm not sure why you have a square root of 2-1, but it is correct I guess.

From this point, multiply x on both sides and use the quadratic formula.

 

[Redbelly98]

Don't forget that:

1. $xL - {\textstyle{1 \over {xC}}} = -R\sqrt {2 - 1} \$ (Note the minus sign for R) may yield a solution as well.

2. You should check all solutions you get in the original equation. Since your work involved squaring both sides of an equation, it is possible to have extraneous solutions.

 

[HallsofIvy]

Multiply both sides by x and you get a quadratic equation for x.