# How do I solve this equation for x?

1. Apr 13, 2012

### p75213

Can somebody point me in the right direction with this?

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

2. Apr 14, 2012

### 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.

3. Apr 14, 2012

### Redbelly98

Staff Emeritus
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.

4. Apr 14, 2012

### HallsofIvy

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