Quadratic Equations are polynomial equations of degree 2. The standard form is:

ax² + bx + c = 0

where a, b, and c are constants and a cannot equal 0.

Three main methods to solve:

1. Factoring — rewrite the equation as a product of two binomials and set each factor to zero.
2. Completing the Square — rearrange the equation into the form (x + p)² = q, then take the square root of both sides.
3. Quadratic Formula — apply the formula directly: x = (-b ± √(b² - 4ac)) / 2a

The Discriminant (b² - 4ac) tells you the number of real solutions:

• Greater than 0 — two distinct real solutions
• Equal to 0 — one repeated real solution
• Less than 0 — no real solutions (complex roots)

Example: Solve x² - 5x + 6 = 0

Factor: (x - 2)(x - 3) = 0, so x = 2 or x = 3