Question 174721
{{{x=sqrt(x)+2}}}
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{{{x-2=sqrt(x)}}}isolating the radical
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{{{(x-2)^2=(sqrt(x))^2}}}squaring both sides
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{{{x^2-4x+4=x}}}multiplying terms
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{{{x^2-5x+4=0}}}combining like terms
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{{{(x-4)(x-1)=0}}}factoring
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x=4 and 1

because we squared these terms we must check for extraneous roots.
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upon checking 1 is thrown out 
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and the final solution is {{{highlight(x=4)}}}