Question

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

Answer 1

Start with
x^2 = 12x − 15
Bring all terms to one side:
x^2 − 12x + 15 = 0
Complete the square: add and subtract 36 (since (12/2)^2 = 36):
(x^2 − 12x + 36) − 36 + 15 = 0
(x − 6)^2 − 21 = 0
So (x − 6)^2 = 21, hence
x − 6 = ±√21
x = 6 ± √21

Solution set: {6 + √21, 6 − √21}