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Melody  11 feb 2022
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2x^2+3x=275

This is a quadratic equation
"Quadratic equations are called quadratic because quadratus is Latin for "square"; in the leading term the variable is squared. "

there are a few different ways of solving quadratic equations. I will show you one of them.
First take all the terms to one side
2x^2 + 3x - 275 = 0

The leading coefficient of 2 (instead of 1) makes it a little harder.

You need to find 2 numbers that multiply to 2*-275 = -550
and add to +3

Since they multiply to a negative number, one has to be negative and the other one positive.
since they add to a positive number, the bigger one will be the positive one.
Since they add to a little number and multiply to a big number, the numbers must be close together in value
Think mainly about the -550 first
10*55 = 550 but they don't add (or subtract ) ot 3
11*50 = 550 still don't add to 3
25*22 = 550 AND 25+-22=+3
so the numbers I am looking for are 25 and -22
I am going to replace the 3x in the middle with -22x+25x
So
2x^2 + 3x - 275 = 0 becomes
2x^2 + -22x + 25x - 275 = 0

now factorise the first 2 and then factorise the second 2 separately
that is
2x(x - 11) + 25(x-11)=0 If you have done it properly, the 2 brackets will be the same.

2x groups of (x-11) + 25 groups of (x-11) => (2x+25) groups of (x-11) => (2x+25) (x-11) =0

(2x+25)*(x-11) =0
now if 2 things multiply together to give 0 then one of them (or both) have to be 0 so
either 2x+25=0 -> 2x=-25 -> x = -12.5
or
x-11=0 -> x=11
So there are 2 answers one is -12.5 and the other is 11.

I don't know how much maths you know - I have tried to break this up into little pieces.
Try to understand it and if you would like me to explain some more, let me know.
This is failrly difficult for this type of question.
4 nov 2013