Question 739215

 {{{sqrt( x + sqrt(x))= sqrt(30)}}}.....raise both sides to power of {{{2}}}


 {{{(sqrt( x + sqrt(x)))^2= (sqrt(30))^2}}}


 {{{ x + sqrt(x)= 30}}}


{{{ sqrt(x)= 30-x}}}



{{{ sqrt(x)= 30-x}}} ...raise both sides to power of {{{2}}} again


{{{ (sqrt(x))^2= (30-x)^2}}}


{{{ x= 30^2-60x+x^2}}}


{{{ 0= 900-60x-x+x^2}}}

{{{ x^2-61x+900=0}}}....use quadratic formula


{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}

{{{x = (-(-61) +- sqrt( (-61)^2-4*1*900 ))/(2*1) }}}


{{{x = (61 +- sqrt( 3721-3600 ))/2 }}}

{{{x = (61 +- sqrt( 121 ))/2 }}}

{{{x = (61 +- 11 )/2 }}}


solutions:

{{{x = (61 + 11 )/2 }}}

{{{x = 72/2 }}}

{{{x = 36 }}}.......since we need {{{ x + sqrt(x)= 30}}}, this is not solution for your problem because {{{36>30}}}


{{{x = (61 - 11 )/2 }}}

{{{x = 50/2 }}}

{{{x = 25 }}}......here {{{25<30}}} and this is your solution

so, {{{sqrt( x + sqrt(x))= sqrt(30)}}} is true for {{{x = 25 }}}