Solve Equations Using Quadratic Formula

When you can't factor or complete the square, you must solve equations using quadratic formula, and GradeA is just the place to learn how to use it!

If you are looking for other ways to solve quadratic equations besides using the quadratic formula, visit how to solve quadratic equations.

Otherwise, you've come to the right place! The great thing about hte quadratic formula is that you can use it even when the problem cannot be factored. GradeA will make this go from complicated formula to a piece of cake. We use simple explanations, complete with colors to make the formula really come to life. Enjoy!


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

Quadratic Formula

Free quadratic equation solver:


What do the letters a, b, and c mean?

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

 quadratic formula: a, b, c?

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.

Example:  5 + 3  
Add: 5 + 3 = 8
    Subtract: 5 - 3 = 2  
    The Answer:  8 or 2  

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

Example: Solve Equations using Quadratic Formula

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

Look at the values for a, b, and c: a = 1, b = 5, c = 6.

Now all we need to do is "plug" the values into the formula:

Quadratic Formula

plugging into the quadratic formula

Now simplify it using the order of operations.

simplifying the quadratic formula

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

Solve equations using quadratic formula

The answer is x = -2 or x = -3.  Because the answers came out as whole numbers, you could have also factored. Need more information on how to factor polynomials?

Additional information

Learning to solve equations using 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.


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