Advance Class Part B: Visual Method

Welcome to Part B of this post. First I am going to show you my visual method how to solve for x. This technique is very useful on the day of the S.A.T. It is not advisable to use this technique in school because by skipping steps you can lose valuable points on an exam. The S.A.T requires no working only answers, so working doesn’t count. Now this visual technique can only be used on certain quadratic equations. The entire purpose of this technique is to save you about 15 seconds, which is a lot in the exam for one question. For student who already did the S.A.T and are going to do over the exam should know how important 15 seconds can be. Now let’s get started. Consider the equation…..

14x^2 - 13x -27 = 0

by just watching the question I can tell the answers are x = -1 and x = 27/14 . There is a special pattern to it. Ok let’s solve this first.

Perform the number splitting method.

14x^2 + 14x – 27x – 27 = 0

Factorize

14x(x +1) – 27(x +1) = 0
(14x – 27)(x +1) = 0
14x = 27…………and x = -1
x = 27/14 ………..and x = -1

Now you must be thinking I solved this question first and wrote the answer…..well I will teach you how to do it.

Remember the number splitting technique, look at that line, do you realize anything about the co efficient. This visual method can only work if and only if the first and last numbers are used in the number splitting. If this condition is met, then the two answers are according to the conditions of the equation.

If the equation is in the form…..:ax^2 –bx + c = 0
The solutions are x = c/a and x = 1

If the equation is in the form…..:ax^2 + bx + c = 0
The solutions are x = -c/a and x = -1

If the equation is in the form……:ax^2 - bx - c = 0
The solutions are x = c/a and x = -1

Now you must be pondering how to remember this? OK simple, the only thing you should be remembering is that you ensure the first and last number is used in the number splitting technique.

How to remember the solutions for x? First write x = c/a and x = 1 (leave a little space to insert any negative signs).To know the sign of x = c/a, watch the sign of b, the sign of c/a is always opposite to b in the equation.To know the sign of x = 1, watch the signs of b and c in the equation. If the signs of b and c are the same the sign of x = 1 is always negative. Now this technique requires lots and lots of practice. I don’t expect you to master this soon but if you do, it will be a great asset to you in the S.A.T.