The expression x^2 + bx + (\frac{b}{2})^2 can be factored as (x + \frac{b}{2})^2, and x^2 - bx + (\frac{b}{2})^2 is (x - \frac{b}{2})^2. These are called perfect squares.
Steps to solve a quadratic equation by completing the square:
Solve 3x^2 - 4x - 1 = 0 by completing the square.
Completing the square is not the most efficient method for solving quadratic equations; the quadratic formula is generally faster.
The quadratic formula is derived by completing the square on the general quadratic equation ax^2 + bx + c = 0.
Completing the square is used for techniques in chapter 2.
These notes cover completing the square, imaginary numbers, and complex numbers, including definitions, operations, and examples.