Question

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

Answer 1

I found: `x=2`

Explanation:

We can try squaring both sides:
`x^(color(red)(2))=(sqrt(6-x))^(color(red)(2))`
and get:
`x^2=6-x`
rearrange:
`x^2+x-6=0`
solve using the Quadratic Formula:
`x_(1,2)=(-1+-sqrt(1+24))/2==(-1+-5)/2`
two solutions:
`x_1=(-1-5)/2=-3` NO (it doesn't work into the original)
`x_2=(-1+5)/2=2` YES