To express the solution to the equation \(3x^2 + 7 = 10\) in set notation, we first solve for \(x\):
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Subtract 7 from both sides: \[ 3x^2 = 10 - 7 \] \[ 3x^2 = 3 \]
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Divide both sides by 3: \[ x^2 = 1 \]
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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 \( { -1, 1 } \).