Question

Solve x2 – 6x + 9 = 0 by completing the square.

A)

x = 3

B)

x = –3

C)

x = 3 and x = –3

D)

x = 1 and x = 9

Answer 1

A.) x = 3

Explanation:

This equation is an example of a perfect square quadratic. This means that the quadratic can be simplified into two of the same factors.

How can you factor the equation? The simplest way is to ask yourself, which two numbers multiply to 9 while also adding to -6? The two numbers which satisfy this question are -3 and -3. Knowing this, you can construct your factors, simplify, and then solve for "x".

x² - 6x + 9 = 0 <----- Expanded equation

(x - 3)(x - 3) = 0 <----- Factored equation

(x - 3)² = 0 <----- Combine both factors

x - 3 = 0 <----- Take square root of both sides

x = 3 <----- Add 3 to both sides