Question 675861
28 doesn't work
{{{sqrt(28) + sqrt(28-7) = 5.29 + 4.58 = 9.87<>7}}}
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16 does, however, work
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{{{sqrt(16) + sqrt(16-7) = 4 + 3 = 7}}}
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Here are the looong, somewhat convoluted steps, which should have been taken when you arrived at 28.  
Obviously, your second solution was much easier to achive than this...
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{{{sqrt(x) + sqrt(x-7) = 7}}}
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{{{(sqrt(x)+sqrt(x-7))^2 = 7^2}}}
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{{{(sqrt(x)+sqrt(x-7))(sqrt(x)+sqrt(x-7)) = 49}}}
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{{{sqrt(x)^2 + sqrt(x)sqrt(x-7) + sqrt(x-7)sqrt(x) + sqrt(x-7)^2 = 49}}}
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{{{x + 2sqrt(x(x-7)) + x-7 = 49}}}
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{{{x + 2sqrt(x^2-7x) + x-7 = 49}}}
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{{{2x + 2sqrt(x^2-7x) = 56}}}
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{{{2sqrt(x^2-7x) = 56 - 2x}}}
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{{{sqrt(x^2-7x) = 28 - x}}}

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{{{sqrt(x^2-7x)^2 = (28-x)^2}}}
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{{{x^2-7x = 784 - 56x + x^2}}}
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-7x + 56x = 784
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49x = 784
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x = 16