Question

Which of the following is a solution of x2 − 6x = –22?

Answer 1

There are many ways in which we can find for the zeros of the problem. We can use the quadratic formula, completing the square, using a graphing calculator, etc.

For this problem, I'll be completing the square.

x² - 6x = -22

Since the constant has been moved to the right side already, we can move on to the next step which is adding (b/2)² to both sides of the equation.

x² - 6x + (-6/2)² = -22 + (-6/2)²

x² - 6x + 9 = -22 + 9

Factor the left side of the equation into a perfect square and simplify the right side.

(x - 3)(x - 3) = -13

Take the square of both sides.

x - 3 = ± √-13

Take out the negative from the square root as the letter "i"

x - 3 = ± i√13

Add 3 to both sides of the equation to let x be by itself.

x = 3 ± i√13

So your two roots will be:

x = 3 + i√13 and x = 3 - i√13

Solution: C. 3 - i√13