Question 265386
{{{ x^(1/2)-(x-5)^(1/2)=2 }}} I've tried every thing I know and I still don't get a real answer. Would you please help me solve it?

sorry, accidentally hit post button before trying to solve it, sorry for inconvenience this may of caused

{{{ x^(1/2)-(x-5)^(1/2)=2 }}}
{{{ (x^(1/2)-(x-5)^(1/2)) (x^(1/2)-(x-5)^(1/2)) = 4  }}} (squared both sides)
{{{ x - (x-5)^(1/2) * x^(1/2) - (x-5)^(1/2) * x^(1/2) + (x-5) = 4 }}}
{{{ x + x - 5 - 2 * ((x-5)^(1/2) * x^(1/2)) = 4 }}} (rearranged)
{{{ 2*x - 2 * ((x-5)^(1/2) * x^(1/2)) = 9 }}}
{{{ - 2 * ((x-5)^(1/2) * x^(1/2)) = 9 - 2*x }}}
{{{ 4 * ((x-5) * x) = (9 - 2*x)(9 - 2*x) }}} (squared both sides)
{{{ 4 * (x^2 - 5*x) = 81 - 36*x + 4*x^2 }}}
{{{ 4*x^2 - 20*x = 81 - 36*x + 4*x^2 }}} 
{{{ 4*x^2 - 4*x^2 - 20*x + 36*x = 81 }}} (rearranged)
{{{ 16*x = 81 }}}
{{{ x = 81/16 }}}
check:
{{{ (81/16)^(1/2) - (81/16 - 80/16)^(1/2) = 2 }}} (5*16=80)
{{{ 9/4 - (1/16)^(1/2) = 2 }}}
{{{ 9/4 - 1/4 = 2 }}}
{{{ 8/4 = 2 }}}