Question

Solve and check for extraneous solutions:
\[x=sqrt{28+9x}-4\]

Answer 1

\[x=\sqrt{28+9x}-4\]

Answer 2

\[x+4=\sqrt{28+9x} \]
\[(x+4)^2=28+9x\]
\[x^2+8x+16=28+9x\]
\[x^2+8x-9x+16-28=0\]
\[x^2-x-12=0\]
\(x+3)(x-4)=0\]

Either x+3=0 or x-4=0
x=-3 or x=4

Therefore both -3 and 4 are solutions of the given equation.