# Solving Quadratic Equations

After identifying a quadratic equation, most of the questions require us to solve them. Meaning, making x or the unknown of the equation as the subject. This post will discuss the necessary skills for students to be able to do that.

**How To Solve Them?**

The "**solutions**" to the Quadratic Equation are where it is **equal to zero**.

They are also called "**roots**", or sometimes "**zeros**"

There are usually 2 solutions (as shown in this graph) and there are a few different ways to find the solutions:

We can Factor the Quadratic (find what to multiply to make the Quadratic Equation)

Or we can Complete the Square

Or we can use the special **Quadratic Formula**:

Just plug in the values of a, b and c, and do the calculations.

We will look at this method in more detail now.

**About the Quadratic Formula**

### Plus/Minus

First of all, what is that plus/minus thing that looks like Â± ?

The Â± means there are TWO answers:

x = [*âˆ’b+âˆš(b2âˆ’ 4ac)] / ***2a**

x = [*âˆ’b-âˆš(b2âˆ’ 4ac)] / ***2a**

**Let's look at the following example**

Solve 5x^2 + 6x + 1 = 0

Coefficients are:a = 5, b = 6, c = 1
Quadratic Formula: x = [*âˆ’b Â± âˆš(b2* *âˆ’ 4ac)] / ***2a**
Put in a, b and c: x = [*âˆ’6 Â± âˆš(62* *âˆ’ 4Ã—5Ã—1)] / ***2Ã—5**

Solve: x = [*âˆ’6 Â± âˆš(36* *âˆ’ 20)] / ***10**
x = [*âˆ’6 Â± âˆš(16)] / ***10**
x = [*âˆ’6 Â± 4] / ***10**
x = âˆ’0.2 **or** âˆ’1