# How to Solve Quadratic Equations Using Formula Method

Quadratic equation is a very common question examiners test candidates or students in any examination most especially WAEC, NECO and JAMB. This is a compulsory question that must be tested on students to examine their understanding on the subject matter.  In one of our posts, we broke down the steps and cited with examples on how to solve quadratic equation using completing the square method. In this post, we will go further on how to solve quadratic equation using formula method popularly known as the almighty formula

Many students run from any calculation course hence the courses that do not require mathematics as a means of admission into tertiary institutions. Mathematics is simple, In fact it is one of the simplest subjects offered in secondary schools if you are determined to learn and concentrate. All that is required is your common sense and reasoning ability.

The West African Examination Council (WAEC) as well as the National Examination Council (NECO) test senior students every academic session on this question and specifically make it mandatory for students to solve quadratic equations using completing the square method because students intentional shy away from the completing the square method of solving quadratic equation due to its complications. The former is the reason we want to teach and break down the best strategy of solving quadratic equations using formula method below. Below are the 4 methods of solving quadratic equations, namely:

1. Formula method (Almighty Formula)
2. Alternative method
3. Graphical method
4. Completing the square method.
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## Simplest Form of Solving Quadratic Equations Using Formula Method

For the sake of this post, we are going to teach you the simplest method on how you can solve any quadratic equations using formula method (almighty formula) amongst the other methods listed above.

Solving a Quadratic equation using formula method require you follow the formula. This method is the simplest means by which you can solve any form of quadratic equations presented to you in any examination of test. Mathematics is no gimmick or magic, understanding the formula makes it easier for you to solve any question you are faced with. Note that examiners may require that you solve a particular quadratic equation using formula method though this is rare because they know it is the shortest means of solving this type of equation so often times they require you make use of completing the square method which has broken down by us if you follow the link in the first paragraph.

NOTE: If you have not been directed by your examiner on the exact method to be adopted in solving quadratic equation, the formula method is the simplest means of solving quadratic equation, so i will advice you adopt it because its is fast and saves time which is quite crucial in any examination.

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With the steps we shall be putting you through below, you should apply it in solving any quadratic equation in WAEC, NECO or any examination you are tested on.

We have broken down the steps needed which starts with knowing the formula. You need to cram the formula properly else solving quadratic equation using formula method would be completely impossible.

## Formula for Solving Quadratic Equation Using Formula Method

Formula => [- b ± √(b² – 4ac)]/2a

Most times when confronted with questions involving quadratic equations, the questionnaire can be specific on the method to be used.

So it’s advisable you take your time to carefully understand the comprehensive solving of this particular method adopted.

## Solving Quadratic Equation using Formula Method

Note the formula;

[- b ± √(b² – 4ac)]/2a

Now lets take a question to solve as an example;

If you are required to solve this quadratic equation => 3x² + 14x + 8 = 0

Recall:
[- b ± √(b² – 4ac)]/2a

The formula contains alphabet a, b & c.

From the equation, we take only the numbers..

:. Let a= 3, b= +14, c= +8

Now we substitute these numbers in place of the alphabets in the formula

[- (+14) ± √{(+14)² – 4(+3)(+8)}]/{2(+3)}

[-14 ± √(196 – 96)]/6

(-14 ± √100)/6

(-14 ± 10)/6

:. (-14 + 10)/6
or
(-14 – 10)/6

:. -4/6 or -24/6

:. -⅔ or – 4

Now we can say that the two values of x are -⅔, -4.

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I believe the above example is well explained. You could be faced with this type of quadratic equation question anywhere and making use of the above steps can guarantee you full marks on any quadratic equation question that mandates you solve it using completing the square method.

Hope the above is well understood? If you still have any questions as regards how to solve quadratic equations using completing the square method in WAEC, NECO, JAMB or any test, please feel free to reach through to us via the comment section below and we shall respond to all questions accordingly.