To solve the equation \( 2x^2 = 32 \), you first divide both sides by 2:
\[ x^2 = \frac{32}{2} \] \[ x^2 = 16 \]
Next, take the square root of both sides:
\[ x = \pm \sqrt{16} \] \[ x = \pm 4 \]
Thus, the solution for \( x \) is:
\[ x = \pm 4 \]
So, filling in the blank, the answer is \( 4 \). Final answer:
\[ x = \pm (4) \]