### Methods to find solutions

### Methods to Solve Quadratic Equations

Below are the four most commonly used methods to solve quadratic equations. Click on any link to learn more about any of the methods.

- The Quadratic Formula (Quadratic formula in depth)
- Factoring (Factoring Method in depth)
- Completing the Square
- Factor by Grouping

A quadratic equation is an equation that can be written as ax ² + bx + c where a ≠ 0

In other words, a quadratic equation must have a squared term as its highest power.

##### Examples of quadratic equations

- y = 2x² + 3x + 5
- y = 13x² + 22
- y = x² − 4x +5
- y = −x² + 5

##### Examples of equations that are NOT quadratic

- y = 11x + 22
- y = x
^{3}− 4x² + 5x + 6 - y = 2x
^{3}− 7x² - y = −x
^{4}+ 5

The solution of a quadratic equation is the value of x when you set the equation equal to zero

Graphically, since a quadratic equation represents a parabola. The solution (for real numbers) is where the parabola cross the x-axis.

When you solve the following general equation: 0 = ax² + bx + c

Given a quadratic equation: ax ² + bx + c

The quadratic formula below will solve the equation for zero

The quadratic formula is: