Set 2x + 8 = -5
2x = -13
x = -13/2 this is in the domain, so it is one solution
Set -x^2 - 3x + 1 = -5
-x^2 - 3x + 6 = 0 multiply through by -1
x^2 + 3x - 6 = 0 complete the square on x
x^2 + 3x + 9/4 = 6 + 9/4
( x + 3/2)^2 = 33/4 take both roots
x + 3/2 = ± sqrt (33)/2
So
x= sqrt (33)/2 -3/2 ⇒ ≈ 1.37 this is in the domain
x = -sqrt (33)/2 - 3/2 ⇒ ≈ -4.37 this is not in the domain
So....the sum of the values =
-13/2 - 3/2 + sqrt (33)/2 =
-16/2 + sqrt (33) /2 =
sqrt (33) - 16
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