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Solve x2 = 12x – 15 by completing the square. Which is the solution set of the equation?

1 Answer

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Answer:

{6-√21, 6+√21}

Explanation:

It usually works well to put the x-terms on one side of the equal sign. Then add the square of half the x-term coefficient.

x^2 -12x = -15 . . . . . . subtract 12x

The x-term coefficient is -12, so the square of half that is (-12/2)^2 = 36. Adding 36, we have ...

x^2 -12x +36 = -15 +36

(x -6)^2 = 21

x -6 = ±√21 . . . . . take the square root

x = 6 ±√21 . . . . . add 6

The solution set is ...

{6-√21, 6+√21}

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