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 find the solution to the equation \( 3x^2 + 7 = 10 \), we first solve for \( x \).

Start by isolating \( x^2 \):

\[
3x^2 + 7 = 10
\]
Subtract 7 from both sides:

\[
3x^2 = 10 - 7
\]
\[
3x^2 = 3
\]
Now, divide both sides by 3:

\[
x^2 = 1
\]
Taking the square root of both sides gives:

\[
x = \pm 1
\]

Thus, the solutions are \( x = -1 \) and \( x = 1 \).

To express these solutions in set notation, we can write:

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

So, the solution set in set notation is:

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