Question 933760: How would I solve sqrt(x)+8=x+2? I have tried squaring both sides but that just leaves me with x+64=(x^2)+4
Answer by richard1234(7193)   (Show Source):
You can put this solution on YOUR website! You didn't square the left-hand side correctly: (sqrt(x) + 8)^2 = x + 64 + 2*8*sqrt(x) = x + 64 + 16 sqrt(x). In general, (a+b)^2 is NOT equal to a^2 + b^2. Remember that.
A slightly simpler solution is to subtract 8 from both sides leaving sqrt(x) = x - 6. Squaring both sides gives x = x^2 - 12x + 36, or x^2 - 13x + 36 = 0. This factors to (x-4)(x-9) = 0, so x = 4 or x = 9. Note that x = 4 is not a valid solution since 4-6 is negative, but the square root returns a non-negative number. Hence the only solution is x = 9.
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