MATH SOLVE

4 months ago

Q:
# Solving a quadratic equation when a is not equal to 1 by completing the square: Consider 8x^2-48x=-104Write the equation so thata=1: x^2+ (blank)x = (blank) * help fill in the blanks and explain how you did it please? thanks

Accepted Solution

A:

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 -13Now, 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 3The solutions are the complex numbers x = 3 ±2i.