Question 833907
{{{ sqrt ( -9x-9 ) + x = 1 }}}
add - x to each side
{{{ sqrt ( -9x-9 ) = -x + 1 }}}
square each side
 {{{-9x - 9 = x^2 -2x + 1}}}
add 9x + 9 to each side
 {{{ 0 = x^2 -2x + 1 +9x + 9 }}}
 {{{ 0 = x^2 + 7x + 10 }}}
factor
{{{ 0 = (x+2)(x+5) }}}
so x = -2 or x = -5
Plug -2 back into the original equation {{{ sqrt ( -9x-9 ) + x = 1 }}}
{{{ sqrt ( -9(-2)-9 ) + (-2) = 1 }}}
{{{ sqrt ( 18-9 ) + (-2) = 1 }}}
{{{ sqrt ( 9 ) + (-2) = 1 }}}
{{{ 3 + (-2) = 1 }}}
So -2 works.
Plug -5 back into the original equation {{{ sqrt ( -9x-9 ) + x = 1 }}}
{{{ sqrt ( -9(-5)-9 ) + (-5) = 1 }}}
{{{ sqrt ( 45-9 ) + (-5) = 1 }}}
{{{ sqrt ( 36 ) + (-5) = 1 }}}
{{{ 6 + (-5) = 1 }}}
-5 works.