In this blog we will see how to Completing the Square. To find the complete square of any term first we need to take a quadratic equation. For example: as we know that the equation which has highest power is 2 is said to be quadratic equation. The general form can be written as: ax2 + bx + c = 0, then change the general form into this given form:
a ( x + d)2 + e = 0.
If we want to find the value of variable ‘d’ then we use formula: the formula to find the vaule of ‘d’ given as: d = b / 2a and formula to find the vlaue of ‘e’ is given as: e = c – b2 / 4a. To calculate the complete square we need to follow some basic steps so that we can easily understand the process.
Step 1: First of all we have to take a simple expression. Suppose we have simple expression as: x2 + bx. Here in this expression value of x is twice.
Step 2: Then complete square in the given expression. So it can be written as: x2 + bx + (b / 2)2 = (x + b / 2)2, it means if we add (b / 2)2 then we get the square.
Let understand all the steps with the help of small example:
For example: p2 + 6x + 7, in this expression the value of b is 6,
Solution: Given expression is p2 + 6x + 7, to find its complete square we need to follow the above mention steps:
First of all we have to find the complete square or value of d. we can find the vlaue of d using the above given formula:
d = b / 2a = 6 / 2
So it can be written as:
p2 + 6p + (6 / 2)2 + 7 – (6 / 2)2
So it can be written as:
(p + 6 / 2)2 + 7 – 9 on further solving we get:
(p + 3)2 – 2. in this way we can find out the complete square.
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