Today we will look at 2 approaches on how to solve quadratic equations. One is a brand new method and the other one is a visual method which I developed through years of practice and experience. Also I am going to show you a very advance method on how to check your answers. I didn’t show you this method before because I wanted you to learn the correct method first and them my shortcuts later on; when you are comfortable with any quadratic equation.
Firstly let’s learn this new method; it is called completing the square. This method is not advisable to use on the S.A.T, but I am teaching people who are also going to school and have problems in mathematics. Some questions in math involve completing the square. Normally these quadratic equations cannot factorize. Let’s look at a question; 2x^2 – 5x + 1 = 0
to begin completing the square you must divide the entire equation by the co efficient of x^2; in this case its 2, so divide throughout by 2.
Dividing by two gives: ………>>> x^2 – (5/2)x + (1/2) = 0
Now have only terms of ‘x’ on the L.H.S.
x^2 – (5/2)x = -(1/2)
Now you must add half the co efficient of ‘x’ and then square that answer to both sides of the equation.
In this case the co efficient of ‘x’ is (5/2), half of that is (5/4) and then that answer squared is (5/4) ^2.
this gives..>> x^2 – (5/2)x + (5/4) ^2 = - (1/2) + (5/4)^2
By doing this step above you have made the L.H.S a perfect square and it can be written in the form (x + (b/2)) ^2. b in this case is – (5/2), so the L.H.S can be written as (x – (5/4) ) ^2.
The equation is now….>> (x – (5/4) ) ^2 = - (1/2) + (5/4)^2
……………………….>> (x – (5/4) ) ^2 = (17/16)
Square root both sides..>> x – (5/4) = +/- sqrt (17/16)
………………………..>> x – (5/4) = +/- (4.123)/4
………………………..>> x = (5/4) +/- (4.123)/4
………………………..>> x = 2.28 and x = 0.22
In my next post I will teach you the cool trick to check your answers and the visual method I perfected!
0 comments:
Post a Comment