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