How do I find the answer to vx+2=x-4

Question

I know the answer is 7, but I can't count on trial and error, or luck , to help me on a test! What's the best method to finding the answer, especially since I need to show my work?

Answer 1

√(x+2)=x-4

square both sides

x+2=x^2-8x+16

x^2-8x+16-x-2=0

x^2-9x+14=0

factor

(x-7)(x-2)=0

x-7=0

x=7 (answer)

x-2=0

x=2 but 2 makes the left side equal to 2 and the right side equal to -2 so disregard the answer of 2 !!!

Answer 2

√(x + 2) = x - 4           square both sides

x + 2 = x² - 8x + 16    set equal to zero

0 = x² - 9x + 14           factor

0 = (x - 7)(x - 2)

 

x ∈ {2, 7}

 

Check:

 

√(2 + 2) = 2 - 4

√4 = -2

±2 = -2                       The validity of the solution depends on the interpretation of √.

 

√(7 + 2) = 7 - 4

√9 = 3

3 = 3