Certainly! Let's solve the equation [tex]\( 3x^2 - \frac{1}{3} = 0 \)[/tex] step by step.
1. Start with the given equation:
[tex]\[
3x^2 - \frac{1}{3} = 0
\][/tex]
2. Isolate the [tex]\( x^2 \)[/tex] term by moving the constant term to the other side of the equation:
[tex]\[
3x^2 = \frac{1}{3}
\][/tex]
3. Divide both sides of the equation by 3 to solve for [tex]\( x^2 \)[/tex]:
[tex]\[
x^2 = \frac{\frac{1}{3}}{3} = \frac{1}{9}
\][/tex]
4. Take the square root of both sides of the equation to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \pm \sqrt{\frac{1}{9}}
\][/tex]
5. Calculate the square root:
[tex]\[
\sqrt{\frac{1}{9}} = \frac{1}{3}
\][/tex]
6. Include both the positive and negative solutions:
[tex]\[
x = \pm \frac{1}{3}
\][/tex]
So, the solutions to the equation [tex]\( 3x^2 - \frac{1}{3} = 0 \)[/tex] are:
[tex]\[
x = -\frac{1}{3} \quad \text{and} \quad x = \frac{1}{3}
\][/tex]
In decimal form, these solutions are:
[tex]\[
x \approx -0.333 \quad \text{and} \quad x \approx 0.333
\][/tex]
Therefore, the solutions to the equation are:
[tex]\[
x \approx -0.333 \quad \text{and} \quad x \approx 0.333
\][/tex]
