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5 August, 23:18

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

A. - 6-i√52

B. - 6+i√13

C. 3-i√13

D. - 3+i√52

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Answers (1)
  1. 6 August, 01:05
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    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
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