Question 816393
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Hi,
{{{sqrt(x+1)=( 5-x)}}} ****    |Squaring both Sides of the EQ
 x+1 = 25-10x + x^2
  x^2  -11x + 24 = 0
 (x-8)(x-3) = 0
  (x-8) = 0  ,  x = 8
0r(x-3) = 0  ,  x = 3

CHECKING our answer***
x = 3,  {{{sqrt(4) = (5-2)= 2}}} 
x = 8   {{{sqrt(9) = (5-9)= -3}}}