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

1 Answer
Sep 14, 2016

Answer:

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