# Linear Equations

• A linear equation is an equation where the highest degree (or power) of the variable (commonly `x`) is one.
• Linear equations have the form `ax + b = 0`; where `a` is the coefficient of `x`, `b` is the constant and `a ≠ 0`.
• Solutions of linear equations are found by isolating `x` on one side of the equation.

• A quadratic equation is an equation in which the highest degree (or power) of the variable (commonly `x`) is `2`.
• Quadratic equations have the form `ax^2 + bx + c = 0`; where `a` is the coefficient of `x^2`, `b` is the coefficient of `x`, `c` is the constant and `a ≠ 0`.
• There are three methods for solving quadratic equations: factoring, using the quadratic formula, and completing the square.

# Factoring

• Factoring to solve for a quadratic equation is the process of writing the equation as two binomial expressions set equal to zero. Once factored, you can set each factor equal to zero and solve for `x`.
• Factoring is best used when all terms are divisible by a common factor or when the equation can be written as a perfect square trinomial.

• The Quadratic Formula: `x = [-b ± sqrt(b^2 - 4ac)] / (2a)`. This method is beneficial for all types of quadratic equations, especially when factoring is not favorable.
• Completing the square method involves rewriting the quadratic equation so that the left-hand side is a perfect square trinomial. This will allow you to write the equation in the form `(x - p)^2 = q`.
Remember: All three methods should lead to the same solutions for `x`. It is critical to familiarize yourself with each method so that you can select the most efficient method based on the given quadratic equation.