Question 453256
{{{x-2-8sqrt(x-1)+15=0}}}, move radical on right, everything else on left
{{{13+x=8sqrt(x-2)}}}, square both sides
{{{(13+x)^2=64(x-2)}}}, calculate
{{{169+26x+x^2=64x-128}}}, move everything to the left side
{{{x^2+26x-64x+169+128=0}}}, combine like terms
{{{x^2-38x+297=0}}}, we now have quadratic equation
:
{{{x = (-(-38) +- sqrt( (-38)^2-4*1*297 ))/(2*1) }}}
{{{x = (38 +- sqrt(1444-1188))/2}}}
{{{x = (38 +- 16)/2 }}}
:
{{{x = (38+16)/2 }}}, x = 27 or {{{x = (38-16)/2 }}}, x = 11