how to factor in order to find a value for a variable.

Question

Solve for x: (give exact answers)

4x^2-3x=1

I factored and got x=1, and -4, but only my x=1 answer was accepted. I have four tries left but I am still unsure on how to find the second answer.

Much help would be appreciated, with steps.

Thanks!

Answer 1

First, be sure that you understand F-O-I-L (First-Outside-Inside-Last).  To use F-O-I-L, we start with:

     (ax+b)(cx+d)

  and go to

     acx² + adx + bcx + bd

 

This problem goes backwards, starting with:

      4x² -3x = 1

      4x² - 3x - 1 = 0                [subtract 1from both sides]

 

All you need to do is find a, b, c, and d.

 

Let's get started --

 

       bd = -1,   so  that is (1)(-1) or else (-1)(1), right?   So we have (......+1)(.......-1 ).

 

Now, we need to find a, b, and c.    [note: there are great procedures for this, but let's stick to trial-and-error for now].

      [note:   4x² - 3x -1  =   4x² - 4x + 1x -1, then reverse F-O-I-L]

 

What factors of 4 [that is, (1,4) or (2,2)] can add to (-3)?     Well  1-4 does. So, put those in and check b and c.

      (4x+1)(x-1) = 0

       4x² -4x + 1x - 1 = 0             [good 'ol F-O-I-L going forward]

       4x² - 3x -1 = 0                    [that's what we want]

 

Here's where the Multiplicative Property of Zero (any number multiplied by 0 is 0) fits in.  Either,

      4x+1=0   or else    x-1=0     or both.

 

If 4x+1=0

     4x=-1                 [add 1 to both sides]

       x=-1/4            [divide both sides by 4]

If x-1=0

       x=1             [add 1 to both sides]   

Answer 2

4x² - 3x = 1

in order to factor it, put 1 in the left side it will transform into -1 and the right side is 0

 

       4x² - 3x - 1= 0  

 

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

                                                   1     -1

                                                  

4x + 1 = 0 or x -1 = 0

 

x = -1/4 or x = 1

Answer 3

Hy Olivia,

 

Use the quadratic formula and the two answers you will end up with are

 

x = -1/4 &  x = 1

Answer 4

Olivia Mayuran is right use quadratic formula

_4x²-3x=1

4x^²+x-x-3x-1=0

4x²+x-4x-1=0

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

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

 

4x+1=0   -->     4x=-1    --> x=-1/4

 

x-1=0     --> x=1

 

I hope it helps