Solve the quadratic equation by completing the square.0 = x2 – 6x + 4–4 = x2 – 6x–4 + 9 = (x2 – 6x + 9)5 = (x – 3)2What are the two solutions of the equation?
Accepted Solution
A:
1) equation given: 0 = x^2 - 6x + 4
2) transpose 4: - 4 = x^2 - 6x
3) complete squares: - 4 = (x^2 - 6x + 9) - 9
4) transpose -9 and factor the square trinomial x^2 - 6x + 9:
- 4 + 9 = (x - 3)^2
5) combine like terms: 5 = (x - 3)^2
6) take square root on both sides: x - 3 = +/- √5
7) transpose - 3: x = 3 +/- √5
Answer: the two solutions are x = 3 - √5 and x = 3 + √5