Solve Equations

Using the Quadratic Formula

When you can't factor or complete the square, you must solve equations using the quadratic formula.  This formula can be used to solve any quadratic equation (even when it does factor).

The Quadratic Formula (Don't worry, we explain how to use it...)

These letters represent the coefficients of the x², x and the constant of the the quadratic equation, respectively.  For clarity, we use colors to represent the different coefficients:  red (x²), blue (x), green (constant).

A coefficient is the number in front ("attached") to the letter.

If there is no coefficient, it means it should be 1. 

Example:  The coefficient of x² is 1.

What does the Symbol  + mean?

The symbol + means you perform both operations, add and subtract.

This means that when you solve equations using the quadratic formula, you should come up with two answers for x.

We will use the problem from above:  x² + 5x + 6 = 0

	a = 1
The picture shown here gives us the following information:	b = 5
	c = 6
Now all we need to do is "plug" into the formula:

Once you have the values substituted into the quadratic formula, simplify it using the order of operations.

Now that you have the equation simplified, evaluate the symbol +.

The answer is x = -2 or x = -3.  You could have also factored.

Learning to solve equations using the quadratic formula is an important skill that you will use throughout your high school math career, and for some of you, your college career. 

You may like to learn how to use algebra tiles.  Algebra tiles are like building a quadratic puzzles.

Return to free algebra help or the GradeA homepage.