Solving a quadratic equation when a is not equal to 1 by completing the square: consider 8x^2-48x=-104 write the equation so that a=1: x^2+ (blank)x = (blank) * fill in the blanks and explain how you did it ?

x² -6x = -13 ⇒ x ∈ {3-2i, 2+2i}

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.

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