Question

Solve the following equations for x. Identify any extraneous solutions. Show all work.

Answer 1

?

Answer 2

You'll want to isolate that radical expression.

Answer 3

Bring that 4 into the right side: \[\sqrt{x+2}=x-4\]
then square both sides: \[x+2=(x-4)^2\]
Expand the right side: \[x+2=x^2-8x+16\]
Express as a quadratic equation: \[x^2-9x+14=0\]
Factor out. The roots are are now obvious. \[(x-7)(x-2)\]
Try substituting 7 & 2 to the original equation and see if both sides are equal.

Answer 4

2 is an extraneous root. Verify it.