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Algebra: How to Use the Quadratic Formula to Solve Quadratic Equations

Updated on August 29, 2016

Step 1

Along with factoring and completing the square, the quadratic formula is an important method to use when solving quadratic equations, particularly when an equation cannot be factored. Using the quadratic formula may seem intimidating at first, but as the following steps demonstrate, it is a very easy process to master. For Step 1, it is important simply to learn the formula as it will not usually be provided on tests and exams.


Step 2

Our quadratic equation is 2x2 + 5x - 7 = 0. As with all quadratic equations, it is represented by ax2 + bx + c = 0. We will use these letter designations to tell us where to insert the numbers into the formula, as shown in illustration #2.


Step 3

Simply continue to solve the equation using the order of operations as shown in illustration #3.


Step 4

Continue solving until we must "split" our equation in two by solving for x with both -5 + 9 and -5 - 9. Divide each by 4 and we have our solutions: 1 and -7/2. Refer to illustration #4 to see this in action.


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