Question

The values \(-1\) and 1 make the equation \(3x^2+7=10\) true. Use set notation to express the solution to the equation.

Answer 1

To solve the equation \(3x^2 + 7 = 10\), we first isolate the quadratic term.

1. Subtract 7 from both sides:

\[
3x^2 = 10 - 7
\]

\[
3x^2 = 3
\]

2. Now, divide both sides by 3:

\[
x^2 = 1
\]

3. Next, take the square root of both sides:

\[
x = \pm 1
\]

Thus, the solution set for the equation \(3x^2 + 7 = 10\) is \( \{-1, 1\} \).

Using set notation, the solution can be expressed as:

\[
\{ -1, 1 \}
\]