show how many solutions are in the solution set for the equation 3x^2 = 21.

Answer 1

To find the number of solutions for the equation \(3x^2 = 21\), we will first solve for \(x\).

1. Start by dividing both sides of the equation by 3:

   \[ x^2 = \frac{21}{3} \] \[ x^2 = 7 \]

2. Now, take the square root of both sides to solve for \(x\):

   \[ x = \pm \sqrt{7} \]

This means there are two solutions:

\[ x = \sqrt{7} \quad \text{and} \quad x = -\sqrt{7} \]

So, the equation \(3x^2 = 21\) has two solutions in the solution set.