Answer:
x=-2 is the only solution
Step-by-step explanation:
The given equation is
[tex]\sqrt{x+6}-4=x[/tex]
Add 4 to both sides of the equation.
[tex]\sqrt{x+6}=x+4[/tex]
Square both sides
[tex]x+6=(x+4)^2[/tex]
[tex]x+6=x^2+8x+16[/tex]
Rewrite in standard form;
[tex]x^2+8x-x+16-6=0[/tex]
[tex]x^2+7x+10=0[/tex]
[tex]x^2+7x+10=0[/tex]
[tex](x+2)(x+5)=0[/tex]
x=-2 or x=-5
Checking for extraneous solution.
When x=-2
[tex]\sqrt{-2+6}-4=-2[/tex]
[tex]\sqrt{4}-4=-2[/tex]
[tex]2-4=-2[/tex]. This statement is true. This implies that: x=-2 is a solution.
When x=-5
[tex]\sqrt{-5+6}-4=-5[/tex]
[tex]\sqrt{1}-4=-5[/tex]
[tex]1-4=-5[/tex]. This statement is not true. This implies that: x=-5 is an extranous solution.
