The concept of completing the square is a topic that you will come around when you are going through the chapter on quadratic equations. We are very much familiar with the standard form of a quadratic expression which can be given as ax.x + bx + c =0. We take the help of completing the square method when we need to convert any given quadratic expression in the vertex form which is given as: a(x – h) (x – h) + k. This method is very helpful and is employed in various other topics too. Proper understanding of the topic of completing the square helps us solve complex problems, thus it is very important that we understand it very clearly. In this article, we will discuss the formula for completing the square and also discuss the various other places where this method is useful.
What is Completing the Square Method?
We learn to find out the roots of an equation in the chapter on quadratic equations. There are different methods through which the roots of a quadratic equation can be obtained. These methods are the square root method, method of factoring, quadratic formula also known as the Sridharacharya formula, and the method of completing the square. Completing the square method in a layman’s language can be explained as the method in which a quadratic equation is changed into a perfect square along with some additional constants attached to the perfect square. We can obtain the roots of a quadratic equation of the form ax.x + bx + c =0 with the help of completing the square method only if a, b, and c are not complex numbers which mean that they should be from those sets of numbers which can be represented on the number line and if a is not equal to the value of 0.
Completing the Square Formula
Completing the square formula can be given as a(x+m) (x+m) + n. The standard equation of ax.x + bx + c =0 is converted into a (x+m) (x+m) + n where m denotes any real number and n denotes constant. The process of conversion is very complex. Instead of going through the complex process, we can find out the complete square with a given formula. For the standard equation ax.x + bx + c =0, we find out the values of m and n first. The value of m = b/2a and the value of n = c – (b.b/4a). We will then put these values in the required equation to obtain the answer.
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Various Other Areas Where Completing the Square Can be Employed
- The first area where this method can be employed is in the conversion of a quadratic equation into the vertex form.
- With the help of this method, a quadratic formula can also be derived.
- The method can be employed in the location of the maximum and the minimum value of any given quadratic equation.
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