Question 635755
{{{sqrt(x-1) = x-7 }}}

{{{(sqrt(x-1))^2 = (x-7)^2 }}}

{{{x-1 = x^2-14x+49 }}}

{{{0 = x^2-14x-x+1+49 }}}...or.......{{{x^2-14x-x+1+49=0 }}}

{{{x^2-15x+50=0 }}}.....use quadratic formula to solve for {{{x}}}

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

{{{x = (-(-15) +- sqrt( (-15)^2-4*1*50 ))/(2*1) }}}

{{{x = (15 +- sqrt(225-200 ))/2 }}}

{{{x = (15 +- sqrt(25 ))/2 }}}

{{{x = (15 +-5)/2 }}}

solutions:

{{{x = (15 +5)/2 }}}

{{{x = 20/2 }}}

{{{x = 10 }}}


or

{{{x = (15 -5)/2 }}}

{{{x = 10/2 }}}

{{{x = 5 }}}


in your case the only solution that works is {{{x = 10 }}}