use the completed square form to factorise the following expression.
14 + 45x - 14x
i know how to solve it with trial and error, but when i put the numbers into completed square form, it is far far too messy to be right. i'm doing something drastically wrong.
would love to be walked through this one.
cheers.
i am taking a levels 10 years since i finished gcse and i think it's becoming a huge hindrance ( i'm working by myself from home ).
i know i'm making small mistakes which are constantly making hard work of things i'm perfectly capable of doing.
i've just done this
4 + 6x - x^2
-->
4 + [( 3 - x )^2 - 9]
-->
( 3 - X )^2 -5
lowest point is -5 when x = 3
the right answer is 13 when x = 3 so i'm clearly making a stupid mistake, as i can see that 9 + 4 is 13 yet can't see how to end up with the right answer. it's getting me down now. anyone know what i'm doing wrong and how i can brush up on it?
original equation
factor out negative one
Now we divide the -6 by 2 and square the result, which is 9; therefore, we will have to add +9 and -9 to the equation within the bracket.
The +9 and the -9 come from the process of completing the square the -4 is from the +4 from the original equation with the -1 factored out
I hope that helps ... If it does not keep asking questions and we will take care of you
really appreciate the help, friend.
i don't recall doing anything like what you have just shown me.
what is this halving and squaring of 6 ( which i know as 'b' ) based on? what equation is it based on?
i have only come across [ a(x + 1/2b )^2 - 1/4b^2 ] + c
Here is a website with a visual representation of completing the square
How to Complete the Square
look at the green box ... it shows all the steps