Certainly! Let's solve the given equation step by step. The equation we have is:
[tex]\[ 6x^2 - 54 = 0 \][/tex]
1. Isolate the [tex]\( x^2 \)[/tex] term:
To isolate [tex]\( x^2 \)[/tex], we first move the constant term to the other side of the equation. So, we add 54 to both sides:
[tex]\[ 6x^2 = 54 \][/tex]
2. Solve for [tex]\( x^2 \)[/tex]:
Next, we divide both sides by 6 to isolate [tex]\( x^2 \)[/tex]:
[tex]\[ x^2 = \frac{54}{6} \][/tex]
The result of this division is:
[tex]\[ x^2 = 9 \][/tex]
3. Solve for [tex]\( x \)[/tex]:
To find [tex]\( x \)[/tex], we take the square root of both sides. Remember, taking the square root of a number results in two values: one positive and one negative. Thus:
[tex]\[ x = \sqrt{9} \][/tex]
Therefore, the solutions are:
[tex]\[ x = 3 \][/tex]
[tex]\[ x = -3 \][/tex]
4. Summary of solutions:
The value of [tex]\( x^2 \)[/tex] is 9, and the solutions for [tex]\( x \)[/tex] are 3 and -3.
In conclusion, the solutions to the equation [tex]\( 6x^2 - 54 = 0 \)[/tex] are:
[tex]\[ x = 3 \quad \text{and} \quad x = -3 \][/tex]
