A free quadratic equation calculator that shows and explains each step in solving your quadratic equation.

- What is a quadratic equation?
- How do I solve a quadratic equation?
- What is the quadratic formula?
- What is a linear equation?
- What is a complex number?

A quadratic equation is any equation that can be written in a form like this: **ax**^{2} + bx + c = 0. In this equation, a, b, and c are constant numbers. The numbers a and b are called coefficients, becaused they are multiplied with x. X is a variable. The equation can be written in different ways, such as **ax**^{2} = -bx - c, but simply rearranging the equation doesn't change the fact that it is a quadratic equation.

Using the quadratic formula,

you can solve for**x** if you know the values of a, b and c.

you can solve for

When you solve a quadratic equation with the quadratic formula, you will always find two solutions. That is because there are always two values of x that satisfy the conditions of the quadratic formula. So you will never find exactly one solution. However, not all solutions are real numbers. When you calculate your solution to your quadratic equation, you might find that you have:

- two real number solutions,
- or, two solutions, both of which are complex numbers.

Try the quadratic equation calculator at the top of this page. Just plug in your values for a, b, and c, and it will calculate your quadratic equation for you. Then, read through the steps that the solver used, to learn and understand how to solve it for yourself.Or, click here for a random example.

The quadratic formula is a way to solve any quadratic equation. If **ax**^{2} + bx + c = 0, then you can solve for **x** using the quadratic formula, which is:

A linear equation is any equation that takes the form: **ax + b = 0**, where a and b are constant numbers and x is a variable. You may be more familiar with it written as **y = mx + b**, where m and b are constants and x and y are variables.

Linear equations are a little easier to solve than quadratic equations, and you solve them in a different way. Since a quadratic equation is any equation that can be written in the form of **ax**^{2} + bx + c = 0, if the value of **a** is zero, then the equation becomes a linear equation, not a quadratic equation.

A complex number is a number that takes the form **a+b***i*, where *i* is the imaginary unit, defined as the square root of -1.

Were you once taught, as I was, that there is no square root of a negative number? Well, that's not exactly true. There is no REAL square root of a negative number. But by defining complex numbers as numbers that involve \(x=\sqrt{-1}\), we get another set of numbers that still follow the laws of mathematics. And complex numbers end up being very useful for solving certain types of problems. Complex numbers each have a **real component,** and an **imaginary component**. As noted above, complex numbers can be written in the form **a=b***i*. Written this way, **a** is the real component, and **b***i* is the imaginary component.

A real number is any number between negative infinity and infinity, or to put it another way, any rational or irrational number.