Question

How do you solve this radical equation: (x+6)^1/2 +6=x?

Answer 1

\[\sqrt{x+6}+6=x\]
\[\sqrt{x+6}=x-6\]
squaring on both sides
\[(\sqrt{x+6})^2=(x-6)^2\]
\[x+6=x^2-12x+36\]
\[0=x^2-12x-x+36-6\]
\[x^2-13x+30=0\]
\[x^2-10x-3x+30=0\]
\[x(x-10)-3(x-10)\]
\[(x-3)(x-10)=0\]
\[x=3,x=10\]