How do you solve x=sqrt(6-x)?

Sep 14, 2016

I found: $x = 2$

Explanation:

We can try squaring both sides:
${x}^{\textcolor{red}{2}} = {\left(\sqrt{6 - x}\right)}^{\textcolor{red}{2}}$
and get:
${x}^{2} = 6 - x$
rearrange:
${x}^{2} + x - 6 = 0$
${x}_{1 , 2} = \frac{- 1 \pm \sqrt{1 + 24}}{2} = = \frac{- 1 \pm 5}{2}$
${x}_{1} = \frac{- 1 - 5}{2} = - 3$ NO (it doesn't work into the original)
${x}_{2} = \frac{- 1 + 5}{2} = 2$ YES