Video Explanation

Text Explanation

First, we square both sides to get rid of the radical.  

(x – 2)² = 10x + 19

x² – 4x + 4 = 10x + 19

x² – 14x – 15 = 0 

(x – 15)(x + 1) = 0 

x = 15 OR x = –1

We've done the algebra correctly and got two solutions, but we can't assume that both work.  We have to check each one in the original equation.  

Check x = 15: 

left side = 15 – 2 = 13

right side =  = 13

The two sides are equal, so x = 15 is valid solution.  

Check x = –1:

left side = (–1) – 2 = –3

right side =  = +3 

Since the radical symbol ( √ ) means to take the positive root only, the two sides have opposite signs and so are not equal.  This means that x =  –1 is not a solution.  

The only solution is x = 15. 

Answer = (C)