How To Solve Quadratic Equations Using Completing The Square Method

The common say “the fear of mathematics is the beginning of wisdom” has misled many potential mathematicians. The thoughts of solving mathematics questions send fear into the minds of many students who rather opt for courses that do not require mathematics as a means of admission into higher institutions. Quadratic equation is one of the most popular mathematics questions students come across in the examination hall or any test and today i will put you through on how to solve quadratic equations using completing the square method.

The West African Examination Council (WAEC) and National Examination Council (NECO) test senior students every year 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 and rather opt for the formula method of solving quadratic equation due to its ease and simplicity.. The former is the reason we want to teach and break down the best method of solving quadratic equations using completing the square method below.

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How To Solve Quadratic Equations Using Completing The Square Method 1

There are actually 4 methods of solving quadratic equations globally, namely:

  1. Completing the square method
  2. Formula method (Almighty Formula)
  3. Graphical method
  4. Alternative method.

Simplest Form of Solving Quadratic Equations Using Completing The Square Method

For the sake of this post, we are going to teach you the simplest way of solving Quadratic equations using completing the square method amongst the other methods listed above.

Solving a Quadratic equation using completing the square method require you follow the formula. Mathematics is no gimmick or magic, understanding the formula makes it easier for you to solve any question you are faced with in WAEC or any examination.

With the steps we shall be putting you through, you should be able to solve even the hardest quadratic equation in WAEC, NECO or any examination.

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 Completing the square method would be completely impossible.

Formula for Solving Quadratic Equation With Completing The Square Method

Formula => [- b ± √(b² – 4ac)]/2a

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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.

E.g: 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.

The above example is quite explanatory. You might be faced with this 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.

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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 out to us through the comment section below and we shall respond to all questions accordingly.

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