To solve the equation [tex]\( 2x^2 = 72 \)[/tex], follow these steps:
1. Divide both sides by 2 to simplify the equation:
[tex]\[
x^2 = \frac{72}{2}
\][/tex]
[tex]\[
x^2 = 36
\][/tex]
2. Take the square root of both sides to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \pm \sqrt{36}
\][/tex]
3. Simplify the square root:
[tex]\[
\sqrt{36} = 6
\][/tex]
So, we get:
[tex]\[
x = \pm 6
\][/tex]
Therefore, the solutions to the equation [tex]\( 2x^2 = 72 \)[/tex] are [tex]\( x = 6 \)[/tex] and [tex]\( x = -6 \)[/tex], which can be written as [tex]\( \{ \pm 6 \} \)[/tex].
Hence, the correct answer is:
[tex]\[
(4) \{ \pm 6 \}
\][/tex]
