Final answer:
The solutions to the quadratic equation x²-8x=-27 are (d) 4 - i√11 and (c) 4 + i√11, as found by applying the quadratic formula.
Step-by-step explanation:
The given equation is x²-8x = -27, which we can rewrite as x²-8x+27 = 0. To find the solution to this quadratic equation, we can use the quadratic formula, which for an equation of the form ax² + bx + c = 0 is given by x = ∛ (-b ± √(b² - 4ac)) / 2a. In this case, a = 1, b = -8, and c = 27.
Plugging these values into the quadratic formula, we get:
x = ∛(8 ± √((-8)² - 4(1)(27))) / (2(1))
x = ∛(8 ± √(64 - 108)) / 2
x = ∛(8 ± √(-44)) / 2
x = (8 ± i√44) / 2
Dividing by 2 gives us two solutions:
x = 4 ± i√11
Therefore, the solutions are (d) 4 - i√11 and (c) 4 + i√11.