ANSWER
x = ± 5i
EXPLANATION
To solve this equation, first, we have to subtract 9 from both sides of the equation,
[tex]\begin{gathered} 2x^2+9-9=-41-9 \\ 2x^2=-50 \end{gathered}[/tex]
Then, divide both sides by 2,
[tex]\begin{gathered} \frac{2x^2}{2}=-\frac{50}{2} \\ x^2=-25 \end{gathered}[/tex]
The next step is to take the square root to both sides of the equation. Remember that i² = -1,
[tex]\begin{gathered} \sqrt[]{x^2}=\pm\sqrt[]{-25} \\ x=\pm\sqrt[]{i^2\cdot25} \\ x=\pm5i \end{gathered}[/tex]
The solutions to this equation are both imaginary - and complementary, and they are x = 5i and x = -5i
