Sure! Let's solve the equation [tex]\(2x^2 - 18 = 0\)[/tex] step-by-step.
1. Start with the given equation:
[tex]\[
2x^2 - 18 = 0
\][/tex]
2. Isolate the [tex]\(x^2\)[/tex] term:
To do this, add 18 to both sides of the equation:
[tex]\[
2x^2 - 18 + 18 = 0 + 18
\][/tex]
Simplifying this, we get:
[tex]\[
2x^2 = 18
\][/tex]
3. Solve for [tex]\(x^2\)[/tex]:
Divide both sides of the equation by 2:
[tex]\[
\frac{2x^2}{2} = \frac{18}{2}
\][/tex]
Simplifying this, we get:
[tex]\[
x^2 = 9
\][/tex]
4. Solve for [tex]\(x\)[/tex]:
Take the square root of both sides of the equation to solve for [tex]\(x\)[/tex]:
[tex]\[
x = \pm \sqrt{9}
\][/tex]
Simplify the square root:
[tex]\[
x = \pm 3
\][/tex]
Therefore, the solutions to the equation [tex]\(2x^2 - 18 = 0\)[/tex] are:
[tex]\[
x = 3 \quad \text{and} \quad x = -3
\][/tex]
So, the solutions are [tex]\(x = 3\)[/tex] and [tex]\(x = -3\)[/tex].
