Final answer:
To solve the equation 2x² - 16x = -50 and find the complex solutions, use the quadratic formula. The solutions to the equation are x = 8 ± (3i√2)/2.
Step-by-step explanation:
To solve the equation 2x² - 16x = -50 and find the complex solutions, we can rearrange it as follows: 2x² - 16x + 50 = 0. Now we can use the quadratic formula, which states that for an equation of the form ax² + bx + c = 0, the solutions are given by x = (-b ± √(b² - 4ac))/(2a). Plugging in the values a = 2, b = -16, and c = 50 into the formula, we get x = (16 ± √(256 - 400))/4. Simplifying further, x = (16 ± √(-144))/4. Since the discriminant (√(b² - 4ac)) is negative, the solutions are complex numbers.
Therefore, the solutions to the equation are x = 8 ± (3i√2)/2.