# Solution of Linear and Quadratic Equations

## Solution of Linear and Quadratic Equations

# 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.

# Quadratic Equations

- 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.

# Quadratic Formula Method

- 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

- 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`

. - This method allows us to derive the quadratic formula and is useful for understanding the graphical transformation of quadratic functions.

**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.