ANSWER
[tex]x=\pm8i[/tex]
EXPLANATION
We want to solve the equation:
[tex]2x^2+128=0[/tex]
This can be solved using the square root method.
To do this, first, separate the terms in the equation:
[tex]2x^2=-128[/tex]
Next, divide both sides by 2:
[tex]\begin{gathered} x^2=-\frac{128}{2} \\ x^2=-64 \end{gathered}[/tex]
Then, find the square root of both sides of the equation:
[tex]\begin{gathered} \sqrt[]{x^2}=\sqrt[]{-64} \\ x=\sqrt[]{64\cdot-1}=\sqrt[]{64}\cdot\sqrt[]{-1} \\ x=\pm8\cdot i \\ x=\pm8i \end{gathered}[/tex]
That is the solution to the equation.
