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To express the solution to the equation \(3x^2 + 7 = 10\) in set notation, we first solve for \(x\):
1. Subtract 7 from both sides:
\[
3x^2 = 10 - 7
\]
\[
3x^2 = 3
\]
2. Divide both sides by 3:
\[
x^2 = 1
\]
3. Take the square root of both sides:
\[
x = \pm 1
\]
This gives us the solutions \(x = 1\) and \(x = -1\).
Now we can express the solution in set notation:
\[
\{ -1, 1 \}
\]
So the solution set is \( \{ -1, 1 \} \).