abs x^2/2 -1 =x+3 solve algebraically

so if I divide through by 2 i get
x^2 -2= 2x+3 simplifying
x^2-2x-5 =0
solve by quadratic formula to get
=3.449 and -0.445 both of which are extraneous roots
if I take negative then I get -x^2 +2=2x+6
simplify to x^2 +2x +4 if taking using quadratic then this does not work either. What have I done wrong

1 answer

x^2/2 - 1 = x+3
x^2 - 2 = 2x+6
x^2 - 2x - 8 = 0

You multiplied x by 2, but not the 3.
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