Let's solve the given equation step-by-step.
The given equation is:
[tex]\[
2x^2 = -18
\][/tex]
Step 1: Simplify the equation by dividing both sides by 2:
[tex]\[
\frac{2x^2}{2} = \frac{-18}{2}
\][/tex]
This simplifies to:
[tex]\[
x^2 = -9
\][/tex]
Step 2: Solve for [tex]\( x \)[/tex]:
We need to find the value(s) of [tex]\( x \)[/tex] such that [tex]\( x^2 = -9 \)[/tex]. To do this, we take the square root of both sides.
Note that taking the square root of a negative number gives us an imaginary number:
[tex]\[
x = \pm \sqrt{-9}
\][/tex]
We know that the square root of [tex]\(-9\)[/tex] can be written using imaginary numbers as:
[tex]\[
\sqrt{-9} = 3i
\][/tex]
Therefore, the solutions for [tex]\( x \)[/tex] are:
[tex]\[
x = \pm 3i
\][/tex]
So, the correct solutions are:
[tex]\[
x = \pm 3i
\][/tex]
From the options given:
1. [tex]\( x = -3 \)[/tex]
2. [tex]\( x = \pm 3i \)[/tex]
3. [tex]\( x = -3i \)[/tex]
4. [tex]\( x = \pm 3 \)[/tex]
The correct answer is:
[tex]\[
x = \pm 3i
\][/tex]
