Answer:
-6 is an extraneous solution.
Step-by-step explanation:
We can start by solving this problem.
First, to remove the square root, we can square both sides.
[tex](x+4)^{2} = x + 10\\x^2 + 8x + 16 = x + 10\\[/tex]
Next, we can subtract both sides by (x+10)
[tex]x^2 + 7x + 6 = 0\\[/tex]
Then, we can factor out the equation.
[tex](x+1)(x+6) = x^2 + 7x + 6 \\= 0[/tex]
Given this, it seems like -1 and -6 would be correct. Plugging this back into the original equation, though,
-1 + 4 = √(-1 + 10)
3 = 3
-6 + 4 = √(-6+10)
-2 ≠ 2
Therefore, -6 is an extraneous solution.
