Question 402199
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Hi
If I m understanding Your question properly:
{{{sqrt(9x + 67) = x+5}}}   |squaring both sides of the equation
   9x + 67 = (x + 5)(x+ 5)
   9x + 67 = x^2 + 10 + 25
  x^2 + x - 42 = 0
factoring
 (x + 7)(x - 6)=0  Note:SUM of the inner product(7x) and the outer product(-6x) =x
 (x + 7)= 0  x = -7
 (x - 6)=0   x = 6
CHECKING our Answer(s)***
 {{{sqrt( 54+67) = sqrt( 121) = 11 = 6 + 5 }}}
 {{{sqrt( -63+67) = sqrt( 4) = 2 = -7 + 5 }}}