How do you solve #sqrt(x-2) + 5=6#?

Question

1359 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-07-15T12:29:58

See a solution process below:

First, subtract #color(red)(5)# from each side of the equation to isolate the radical while keeping the equation balanced:

#sqrt(x - 2) + 5 - color(red)(5) = 6 - color(red)(5)#

#sqrt(x - 2) + 0 = 1#

#sqrt(x - 2) = 1#

Next, square each side of the equation to eliminate the radical while keeping the equation balanced:

#(sqrt(x - 2))^2 = 1^2#

#x - 2 = 1#

Now, add #color(red)(2)# to each side of the equation to solve for #x# while keeping the equation balanced:

#x - 2 + color(red)(2) = 1 + color(red)(2)#

#x - 0 = 3#

#x = 3#