Certainly! Let's solve the equation [tex]\( 6x^2 = a \)[/tex] step-by-step.
1. Introduction to the Problem:
- We are given the equation [tex]\( 6x^2 = a \)[/tex].
- Our goal is to solve for [tex]\( x \)[/tex].
2. Isolate [tex]\( x^2 \)[/tex]:
- First, we need to isolate the term [tex]\( x^2 \)[/tex] on one side of the equation. We do this by dividing both sides of the equation by 6.
[tex]\[
x^2 = \frac{a}{6}
\][/tex]
3. Solve for [tex]\( x \)[/tex]:
- Next, we take the square root of both sides of the equation to solve for [tex]\( x \)[/tex]. It's important to remember that the square root of a number has both a positive and a negative solution.
[tex]\[
x = \pm \sqrt{\frac{a}{6}}
\][/tex]
4. Substitute the given value of [tex]\( a \)[/tex]:
- Let's assume a value for [tex]\( a \)[/tex]. In our case, let [tex]\( a = 24 \)[/tex].
5. Calculate [tex]\( x \)[/tex] with the given [tex]\( a \)[/tex]:
- Substitute [tex]\( a = 24 \)[/tex] into the equation.
[tex]\[
x^2 = \frac{24}{6} = 4
\][/tex]
- Now, take the square root of 4.
[tex]\[
x = \pm \sqrt{4}
\][/tex]
- Simplify the square root of 4.
[tex]\[
x = \pm 2
\][/tex]
6. Conclusion:
- The solutions for [tex]\( x \)[/tex] are [tex]\( x = 2 \)[/tex] and [tex]\( x = -2 \)[/tex].
Therefore, the solutions for the equation [tex]\( 6x^2 = a \)[/tex] when [tex]\( a = 24 \)[/tex] are [tex]\( x = 2 \)[/tex] and [tex]\( x = -2 \)[/tex].
