Is arithmetic only about additions?

Square addition

We will deal with the square addition in this article. In this context, it explains what the square extension is used for and shows some examples. This article is part of our math section.

In mathematics, the quadratic addition is a method for transforming terms in which a variable occurs as a square, for example x2 or a2. The aim is to create a squared binomial. For a better understanding, I recommend reading the following articles. Although this is not absolutely necessary, it often helps to better understand the square extension.

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Square addition: Explanation and examples

Schoolchildren and often also students appreciate it when they are given a "timetable" with which they can solve a task. The following procedure can be used, for example, in order to carry out the addition of the square and then to form appropriate brackets:

  1. If the number in front of the square variable is not 1, divide by this.
  2. Finds out p (this is the number in front of the simple variable)
  3. Now forms (p: 2)2. This gives you the square extension
  4. In your equation, move the single number without a variable to the other side
  5. Build the quadratic complement into the equation
  6. Forms the expression in brackets

That’s the theory. The following examples demonstrate the practical procedure. You can find a comprehensive explanation below the invoice.

Example 1:

We first divide the equation 2x2 -8x -4 = 0 by the number in front of x2, so by 2 and get x2 -4x - 2 = 0. Now we read off "p", this is the number in front of the x and in our example this is the number -4. We put this in the formula (p: 2)2 one and get (-4: 2)2 = 4. The number 4 is our square addition.

Next we create the "-2" on the right side and get x2 -4x = 2. Now we use the quadratic addition "4" that we already calculated above and add it to both sides of the equation. The formation of the expression in brackets is still missing. In the brackets we write an x ​​and behind it now p: 2, i.e. -4: 2 = -2. Don't forget the square behind the bracket. Sample: Multiply becomes (x - 2)2 off again, we get the starting equation again. So we have formed an expression in brackets.

Example 2:

Here, too, we first divide by the number in front of x2, so by 3. Then we read off p = 1.6666 ... and calculate the quadratic addition to 0.694. We create the 0.66666 of the equation on the right hand side and add the square complement on both sides of the equation. Now we form the bracket in which x is and 1.6666: 2 = 0.83333 ...

Example 3:

Here, too, we divide by the number in front of the square, i.e. by 8. Then we find p = 0.5 and determine the square addition to 0.0625. We add these on both sides of the equation. And then we form the bracket with a and p: 2 = 0.5: 2 = 0.25.

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