How do you find x in this equation? sqrt(x+11) = sqrt(x)+1

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For this problem, you are going to square both sides of the equation:

(sqrt(x+11))^2=(sqrt(x)+1)^2

Which gives us:

x+11 = x+2sqrt(x) +1

We will then subtract both x and 1 from both sides of the equation giving us:

x+11-x-1 = x+ 2sqrt(x)+1-x-1

Then combine like terms:

10 = 2 sqrt(x)

Divide both sides by 2:

5=sqrt(x)

And square both sides again:

25 = x

Then check the answer in the original equation to see if it is extraneous:

sqrt(25+11) = sqrt(25)+1

sqrt (36) = 5+1

6=6

It checks!

sqrt(x+11) = sqrt(x)+1

Square both sides:

x+11 = x+2sqrt(x) +1

Reduce similar:

10=2sqrt(x)

Divide by 5:

==> sqrt(x) = 5

==> x= 25

Now to check your answer:

sqrt(25+11) = sqrt(25)+1

sqrt(36) = 5+1

6= 6

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