Let x be the number
[tex]x - 10 = \sqrt{7x + 8} \\ {(x - 10)}^{2} = { \sqrt{7x + 8} }^{2} \\ {x}^{2} - 20x + 100 = 7x + 8 \\ {x}^{2} - 20x + 100 - 7x - 8 = 0 \\ {x}^{2} - 27x + 92 = 0 \\ (x - 23)(x - 4) = 0 \\ \\ x - 23 = 0 \\ x = 23 \\ \\ x - 4 = 0 \\ x = 4[/tex]
Therefore the number is 23 or 4.
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