Answer:
x=-2 and x=-3
Step-by-step explanation:
\(\sqrt{x+3} -4= x-1\)
Solve the equation for x
Add 4 on both sides
\(\sqrt{x+3}= x+3\)
Now take square on both sides
\(x+3= (x+3)^2\)
\(x+3= (x+3)(x+3)\)
\(x+3= x^2+6x+9\)
\(x=x^2+6x+6\)
\(0=x^2+5x+6\)
\(0=(x+3)(x+2)\)
x+3=0, x=-3
x+2=0, x=-2
LEts plug in -2 for x and verify the solution
\(\sqrt{x+3} -4= x-1\)
\(\sqrt{-2+3} -4= -2-1\)
\(\sqrt{1} -4=-3\)
\(-3=-3\) True
Plug in x=-3
\(\sqrt{-3+3} -4= -3-1\)
\(\sqrt{0} -4=-4\)
\(-4=-4\) True
So x=-2 and x=-3 are the non extraneous solution
