Answer:
x² -6x = -13 ⇒ x ∈ {3-2i, 2+2i}
Step-by-step explanation:
To make a=1, divide the equation by the coefficient of x², which is 8.
... x² -6x = -13 . . . . . . your blanks are filled with -6 and -13
Now, to complete the square, add the square of half the x-coefficient:
... (-6/2)² = 9.
... x² -6x +9 = -4 . . . 9 added to both sides
... (x -3)² = -4 . . . . . rewrite as a square
... x -3 = ±2i . . . . . . take the square root
... x = 3 ±2i . . . . . . . add 3
The solutions are the complex numbers x = 3 ±2i.
