Solving Quadratic Equations: Methods and Examples

This page presents a comprehensive overview of solving quadratic equations through various methods, including factoring and the quadratic formula. The content is structured around three detailed examples that progressively increase in complexity.

Definition: Difference of squares is a binomial where both terms are perfect squares and are subtracted, following the pattern a² - b² = (a+b)(a-b).

Highlight: The degree of an equation determines the number of solutions it will have.

Example One demonstrates solving x² = -4x:

Example: The solution process involves:

1. Writing in standard form
2. Factoring out GCF
3. Setting factors equal to zero Solutions: x = 0 and x = -4

Example Two shows solving x² = -4x + 5:

Example: Key steps include:

1. Standard form arrangement
2. Discriminant checking
3. Factoring Solutions: x = 1 and x = -5

Example Three tackles 3x² + 11x - 6:

Vocabulary: Discriminant - a value that helps determine the nature of solutions in a quadratic equation.

Highlight: The quadratic formula is essential when factoring isn't immediately obvious.