Hello there!
There are 2 solutions.
2 and -2
Reason:
There is never one solution in this kind of problem (x is squared), as there always has to be the positive form and the negative form (a negative squared is a positive and a positive square is a positive)
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Work:
2x^2 + 8 = 0
Subtract 8 from each side
2x^2 + 8 = 0
-8 -8
2x^2 = -8
now, divide both sides by 2
(2x^2)/2 = -8/2
x^2 = -4
now, we must take the square root of each side
√x^2 = √-4
x = 2/-2
I hope I helped!
~ Fire