Let's solve the equation [tex]\(3x^2 - 27 = 0\)[/tex] step by step using square roots.
1. Move the constant term to the other side of the equation:
We start with the given equation:
[tex]\[
3x^2 - 27 = 0
\][/tex]
Add 27 to both sides to isolate the [tex]\(x^2\)[/tex] term:
[tex]\[
3x^2 = 27
\][/tex]
2. Divide both sides by the coefficient of [tex]\(x^2\)[/tex]:
To isolate [tex]\(x^2\)[/tex], divide both sides of the equation by 3:
[tex]\[
x^2 = \frac{27}{3}
\][/tex]
Simplify the right-hand side:
[tex]\[
x^2 = 9
\][/tex]
3. Take the square root of both sides to solve for [tex]\(x\)[/tex]:
To solve for [tex]\(x\)[/tex], take the square root of both sides of the equation. Remember that taking the square root yields two solutions, a positive and a negative:
[tex]\[
x = \pm \sqrt{9}
\][/tex]
Simplify the square root:
[tex]\[
x = \pm 3
\][/tex]
So, the solutions to the equation [tex]\(3x^2 - 27 = 0\)[/tex] are:
[tex]\[
x = 3 \quad \text{and} \quad x = -3
\][/tex]
Thus, the correct answers are [tex]\(\pm 3\)[/tex].
