Solving Quadratics (All methods)

A quadratic equation is a polynomial equation of degree 2, typically in the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

The methods to solve quadratic equations include factoring, using the quadratic formula, completing the square, and graphing.

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation.

To factor a quadratic equation, find two numbers that multiply to ac (the product of a and c) and add to b (the coefficient of x).

Completing the square involves rewriting a quadratic equation in the form (x - p)² = q, making it easier to solve.

The roots of a quadratic equation are the values of x that make the equation equal to zero.

Rearrange to x² + 10x + 9 = 0, then factor to (x + 1)(x + 9) = 0, giving roots x = -1 and x = -9.

Factor to 3(x + 2)(x - 4) = 0, giving roots x = -2 and x = 4.

Using the quadratic formula, x = (26 ± √(26² - 4*7*(-8))) / (2*7), resulting in x = 4 and x = -2/7.

Taking square roots gives x + 1 = ±5, leading to solutions x = 4 and x = -6.