Another factoring question...?

Question

2x^2-7x=4

I understand that you should subtract four from both sides, but after that, I don't know where to go. Would you mind explaining how this works?

Thanks so much!

Answer 1

We want to make the expression look like something we recognise and know how to deal with so in this case, we want the expression to equal zero (you'll see why later)

To do this we need to subtract 4 from either side so we are left with:

2x^2 - 7x - 4 = 0

Our aim is to find the numbers which x could represent so that this statement is still true.

The next step is to 'factorise' the equation which means find the two things that you multiply together to get the above expression.

(2x + 1 )(x -  4) = 0

From this we can see that either '2x + 1' = 0 or 'x - 4' = 0.

Now if 2x + 1 = 0

Then x = -1/2

And if x - 4 = 0

Then x = 4.

Now we are left with x = -1/2 or 4.

If there's anything else you need, just ask.  

Answer 2

2x^2 - 7x  - 4 = 0

(2x + 1)(x - 4) = 0 -------->2 # that will give u -7 ( -8 + 1 )

2x + 1 = 0 ---->change sign on 1, then move to the other side

2x = -1 -------> divided both side by 2

x = -1/2

x - 4 = 0 ---->change sign on -4, then move to the other side

x = 4

Answer 3

firstly put all terms on one side:

2x^2 - 7x - 4 = 0

lets break it down to :

2x^2 - 8x + 1x - 4 = 0     (since -8 + 1 = -7)

now we take out the common factors: 2x is common to the first 2 terms and 1 is common to the last two terms

2x ( x - 4 ) + 1 ( x - 4 ) = 0

now since (x - 4) is common to both sides, we can factorize that into

(x - 4 )(2x + 1) = 0

so x - 4 = 0

x = 4

and 2x + 1 = 0

2x = -1

x = -1/2

Get it?

Answer 4

Ok the answer is (2x+1)(x-4)=0

How to get it from 2x^2-7x-4=0

to get the 2x^2 term we need a 2x and an x --> (2x   )(x    )

then looking at the term without x i.e. 4 we know we need either a 1 and a 4 (1*4=4) or a 2 and a 2 (2*2=4) we also know that because the 4 is negative we need one positive and one negative non-x value ---> (2x - ) (x + ) or (2x + ) (x - )

Now we just need to notice that -7 = (2*-4)+(1*1) and the answer follows

To solve the equation we find two values of x where the bit in brackets is zero. The first term (2x+1) is zero when x=-0.5 and the second term (x-4) is zero when x=4 and there are the two values of x that satisfy the equation.

Hope that helps!