Solving Quadratic Equations: Algebra Revision Guide Subject: Mathematics | Grade: Grade 7-9 A quadratic equation is a second-degree polynomial equation in a single variable, written in the standard form: Where $a \neq 0$. There are three primary methods to solve these equations: Solving by Factoring Factoring involves rewriting the quadratic expression as a product of two linear binomials. • Example: Solve $x^2 - 5x + 6 = 0$ • Find two numbers that multiply to $6$ and add to $-5$. These are $-2$ and $-3$. • Rewrite the equation: $(x - 2)(x - 3) = 0$ • Set each factor to zero: $x - 2 = 0 Rightarrow x = 2$ or $x - 3 = 0 Rightarrow x = 3$. Completing the Square This method involves transforming the equation into a perfect square trinomial. Move the constant term to the other side: $x^2 + bx = -c$ Add $( rac{b}{2})^2$ to both sides. Factor the perfect square trinomial and solve by taking square roots. The Quadratic Formula The quadratic formula can solve any quadratic equation. It is derived by completing the square on the standard form: Sample Problem Solve $x^2 - 4x - 5 = 0$