Completing the square

falcao12

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2017-09-13 20:10

Hello all my friends from the Steemit community, I was away for work reasons, now back I want to share with you a very simple mathematical technique known as square completions that help us solve equations such as:

Step 1

Adding and subtracting the quotient square (the division / fraction), the coefficient of x between 2

Step 2

By grouping terms, you will get a perfect square trinomial. The terms x^2 , bx and + b^2/22

Step 3

Factoring (reducing) this trinomial to a squared binomial, which was obtained: (1) extracting the square root of the first term from the trinomial sqrt(x^2) = x, which will be the left-hand side of the binomial; (2) by extracting the square root of the third term from the trinomial sqrt(b^2/22) = b/2, which will be the right term of the binomial; (3) using the sign of the second term of the trinomial + bx as the sign separating the terms of the new binomial

Here I leave an example of the application of this technique which is very useful when we just want to clear the variable and not find the roots of the quadratic function.