Question 188921
{{{ sqrt (2x+1) }}} - {{{ sqrt (x+1) }}} = 2


Can someone show me how to solve the problem by first isolating {{{ sqrt (2x+1) }}} on the left side of the equation and then squaring each side? 


So the first step gives us...
{{{ sqrt (2x+1) }}} = 2+ {{{ sqrt (x+1) }}}


Now how do I square each side of this equation and find all solutions of x?
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Square both sides
(2x+1) = 4 + 4sqrt(x+1) + (x+1)
Collect terms, isolate the sqrt
x = 4 + 4sqrt(x+1)
x-4 = 4sqrt(x+1)
Square again
x^2 - 8x + 16 = 16(x+1) = 16x + 16
x^2 - 24x  = 0
x*(x-24) = 0
x = 0 (extraneous solution, ignore it)
x = 24