# 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 ± ?

The ± means there are TWO answers:

x = [*−b+√(b2− 4ac)] / ***2a**

x = [*−b-√(b2− 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 = [*−b ± √(b2* *− 4ac)] / ***2a**
Put in a, b and c: x = [*−6 ± √(62* *− 4×5×1)] / ***2×5**

Solve: x = [*−6 ± √(36* *− 20)] / ***10**
x = [*−6 ± √(16)] / ***10**
x = [*−6 ± 4] / ***10**
x = −0.2 **or** −1