factoring quadratics...?

Question

how do you factor this equation: 4x^2+7x=2 please explain how...

sure i no the quadratic formula but i need to solve this equation using the factoring method...

Answer 1

Well, you subtract two from both sides, first of all.
So.... 4x^2+7x-2=0
Then.... you have to go through a process of elimination to see what works by setting the eqn. up thusly...
( )( )=0
so... lets say (4x- )(x+ )=0, which takes care of the first factor, now you must worry about inserting the 7x and the -2 into this new form of the eqn. So...let's try
(4x-1)(x+2)=0
....you can check this by multiplying the parenthesis....so
(4x)(x)= 4x^2, which is your 1st factor
(4x)(2)-(1x)= 7x, which is your second factor
(-1)(2)= -2, which is your final factor...
so the new form of the eqn is indeed (4x-1)(x+2)=0, hopefully you can solve it from here....

Answer 2

First, you set the equation equal to zero, which gives 4x^2+7x-2=0. Next, you try to find factors of 4 and 2 that will give you a 7x when the middle terms are added together. The only two factors for the 2 are 1 and 2, and one of them has to be negative. Since the middle number is 7, it is easy to see that we can get 7 by multiplying the 4 and the 2 to get 8, then subtracting 1, so our factors for 2 are -1 and 2, so we get (4x-1)(x+2).

Answer 3

The first thing to do in this problem is to subtract 2 from both sides so that you end up with 4x^2+7x -2=0
Next, because of the 4x^2 you know that in one of the parentheses, there needs to be either (2x +/- something)(2x +/-something) or (4x +/- something)(x +/- something). Using one of these, you need to figure out the other number in the parenthases, so that something that multiplies to 2 can be multiplied times the coefficients with x and those numbers can add up to seven. (using FOIL, that's the outside times the inside part). Luckily, there are only 2 possibilities of two numbers multiplying to -2 and those are 2 and -1 and -2 and 1. If we used the (2x+1)(2x-2), it would not multiply out to the original equation, so the combination of 4x and x must be used. Since the 7x is positive, the 4x must be multiplied by positive 2 and the x by -1, so your final equation would be (4x-1)(x+2). If you want to check it using FOIL, (4x)(x)=4x^2, 2(4x)+-1(x)=7x and (-2)(1)=-2, giving you the original equation of 4x^2+7x-2.

Sorry, I know it's confusing, but you will get it eventually :)

Answer 4

Get all your terms onto one side so you have 4x^2 + 7x - 2 = 0.

The you can use the quadratic formula. Just Google it if you don't know it. The plug in the numbers for the letters and solve.

a = 4x^2
b = 7x
c = -2

Answer 5

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

Answer 6

4x^2+7x-2=0
(4x-1)(x+2)
x=1/4 Or -2

Answer 7

if you have an equation this type ax^2+bx+c=0 you can rewrite it as a(x-x1)(x-x2)=0 ; x1, x2 are the solutions of the equation

so,in your case you first rewrite as:
4x^2 +7x -2=0
x1,2= (-7 +/- sqrt (81) ) / 2*4 = (-7+/- 9)/8
x1=1/4
x2= -2
and then your equation gets:
4(x -1/4 )(x+2)=0

Answer 8

4x^2+7x-2=4x^2+8x-x-2=4x(x+2)-1(x+2)=(x+2)(4x-1). answer
obs: 4x()(-2)=8x(-1).