To determine the number of solutions in the solution set for the equation \( 3x^2 = 21 \), we must first solve the equation. Here is the step-by-step process:
1. Divide both sides of the equation by 3 to isolate the \( x^2 \) term:
\( \frac{3x^2}{3} = \frac{21}{3} \)
\( x^2 = 7 \)
2. Next, we take the square root of both sides to solve for x. Remember that taking the square root will give us two solutions: one positive and one negative.
\( \sqrt{x^2} = \pm\sqrt{7} \)
\( x = \pm\sqrt{7} \)
This gives us two real solutions for x: \( x = \sqrt{7} \) and \( x = -\sqrt{7} \).
Thus, the solution set for the equation \( 3x^2 = 21 \) contains two solutions.
Show how many solutions are in the solution set for the equation 3x2=21
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