How do you solve #7= 2+ \sqrt { x + 7}#?

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Answer 1 · 2017-05-27T02:07:58

See a solution process below:

First, subtract #color(red)(2)# from each side of the equation to isolate the radical while keeping the equation balanced:

#-color(red)(2) + 7 = -color(red)(2) + 2 + sqrt(x + 7)#

#5 = 0 + sqrt(x + 7)#

#5 = sqrt(x + 7)#

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

#5^2 = (sqrt(x + 7))^2#

#25 = x + 7#

Now, subtract #color(red)(7)# from each side of the equation to solve for #x# while keeping the equation balanced:

#25 - color(red)(7) = x + 7 - color(red)(7)#

#18 = x + 0#

#18 = x#

#x = 18#