Example: The equation 2x² - 3x - 5 = 0 is solved step by step, beginning with dividing all terms by 2

Vocabulary: A perfect square trinomial is an expression that can be written as $x + p$²

Highlight: The method involves adding and subtracting specific terms to create a perfect square, leading to solutions x = 5/4 or -1

Definition: The quadratic formula x = $-b±√(b²-4ac)$/2a solves any equation in the form ax² + bx + c = 0

Example: For 2x² + 6x - 8 = 0, where a=2, b=6, and c=-8, the solution process demonstrates the formula's application

Highlight: The method yields solutions x = 1 or -4, showing how the formula can efficiently solve equations that might be challenging with other methods

Example: x² + 8 + 16 = 0 is solved through factorization by rearranging terms into x$x+4$ + 4$x+4$ = 0

Definition: Factorization is the process of breaking down a quadratic expression into the product of its factors.

Highlight: The solution x = -4 appears twice in this example, indicating a repeated root.