About Completing the Square Formula
A method for turning a quadratic formula of the form ax2+ bx + c to the vertex form a(x - h)2+ k is known as completing the square. Solving a quadratic equation is the most common use of completing the square. This can be accomplished by rearranging the expression a(x + m)2+ n obtained after completing the square, so that the left side is a perfect square trinomial. To get all the Maths formulas check out the main page.
Completing the Square Formula
Factoring a quadratic equation, and thus finding the roots and zeros of a quadratic polynomial or a quadratic equation, is the most typical use of the completing the square method. The factorization approach can be used to solve a quadratic equation of the type ax2+ bx + c = 0. However, factoring the quadratic formula ax2+ bx + c is sometimes difficult or impossible. To better grasp this situation, consider the following scenario.
For example:
We can't factorise x2+ 2x + 3 because we can't find two numbers whose sum is 2 and whose product is 3. In such circumstances, we complete the square and write it as a(x + m)2+ n. We claim we've "finished the square" here because we have (x + m) full squared.
Completing the Square Formula
A methodology or approach for converting a quadratic polynomial or equation into a perfect square with an additional constant is known as the square formula. By using completing square formula or approach, a quadratic expression in variable x: ax2+ bx + c, where a, b, and c are any real values except a ≠ 0, can be turned into a perfect square using one additional constant.
Completing the square formula is a methodology or procedure for finding the roots of specified quadratic equations, such as ax2+ bx + c = 0, where a, b, and c are all real values except a ≠ 0.
Formula for Completing the Square:
The formula for completing the square is: ax2+ bx + c ⇒ a(x + m)2+ n
where, m is any real number and n is a constant term.
Instead of employing a complicated step-by-step procedure to construct the square, we can utilise the following simple formula. Find the following to complete the square in the phrase ax2 + bx + c:
m = b/2a and n = c - (b2/4a)
Substitute these values in: ax2+ bx + c = a(x + m)2+ n.
Solved example of the use of Completing the Square Formula
Example: Find the number that needs to be added to x2 - 7x to make it a perfect square trinomial using the completing the square formula.
Sol: since the given expression is x2- 7x.
Method 1: On comparing the expression with ax2+ bx + c, we have a = 1; b = -7
By using the formula, the term that should be added to make the given expression a perfect square trinomial is,
(b/2a)2= (-7/2(1))2= 49/4.
The term that should be added to make the following expression a perfect square trinomial, according to both techniques, is 49/4.
Method 2:
x has a coefficient of -7. -7/2 is half of this number. (-7/2)2 = 49/4 is the square.
Pdf of Completing the Square Formula
