Quadratic equations are a special kind of equation that come in two forms:

$$ax^2 + bx + c = 0$$ $$(x - \alpha)(x - \beta) = 0$$

Difference from linear equations

As you may know already, an equation’s roots are the x-coordinates where the curve of the equation touches the x-axis ($y = 0$). Linear equations make straight lines so they only have a single root, whereas quadratic equations can have two roots and form a curve, therefore they are not linear.

Solving

To find the value of x, we can use one of the following methods:

Using the quadratic formula

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

By completing the square

To complete the square for a quadratic, you half the coefficient of the $x$ and replace the $x^2$ with $(x + \frac{a}{2})^2$

For example, with the quadratic:

$$x^2 - 4x + 8 = 0$$

You half the $-4$ to get $-2$ then put this in the square: