Question

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

(negative 6 minus StartRoot 51 EndRoot comma negative 6 + StartRoot 51 EndRoot)
(negative 6 minus StartRoot 21 EndRoot comma negative 6 + StartRoot 21 EndRoot)
(6 minus StartRoot 51 EndRoot comma 6 + StartRoot 51 EndRoot)
(6 minus StartRoot 21 EndRoot comma 6 + StartRoot 21 EndRoot)

Answer 1

(d) (6-√21, 6+√21)

Explanation:

You want the solution to x² = 12x -15 by completing the square.

Completing the square

The square of a binomial is ...

(x -a)² = x² -2ax +a²

The constant at the end of this expression is the square of half the x-coefficient. We use this fact to "complete the square."

x² = 12x -15 . . . . . . given

x² -12x = -15 . . . . . the x-coefficient is -12. We want to add (-12/2)² = 36

x² -12x +36 = -15 +36

(x -6)² = 21

Solution

To solve this equation, we take the square root:

x -6 = ±√21

x = 6 ±√21 . . . . . . add 6

The solution set is {6-√21, 6+√21}.

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