factor 2x^2+x-14

Question

Please help me factor this.

Answer 1

2 X^2 + X - 14 

 

 

2 ( X^2 + 1/2 X - 7)         

 

   Should factor to :

 

 2 ( X + a) ( X+b)    / in such a way that  a.b = -7   a+ b = 1/2 , there is no rational numbers that that

 

                                 meet that criteria , so factor it with completing the square.

 

2 ( X^2 + 1/2 X + 1/16 - 1/16 - 7 ) =

 

2[ ( X + 1/4 ) ^2 - 113/16) ] =

 

2  ( X + 1/4 - √113/4) ( X + 1/4 + √113/4) =

 

2 ( X +1/4 + √(113/16)( X + 1/4 -(√113/16 )

 

2 ( X + ( (1 + √(113)/4) ( X + (( 1 - √113)/4)

Answer 2

This can be done most easily with the quadratic equation

(1/ (2*a) )*( -(b) ± √(b^2 - 4*a*c) )

 

where our original expression is interpretted

 

ax^2 + bx + c

 

            = 2x^2 + x - 14

and so a=2, b=1, and c=-14.

Answer 3

2x² + x - 14

 

Using the quadratic formula;

 

x =   -b ± √ (b² - 4ac)    

             2a

 

where a = 2, b = 1 and c = 14

 

x =   -(1) ± √ ((1)² - 4(2)(14))
                        2(2)

 

x =  -(1) ± √ (1 - 112)
                    4

 

x = -(1) ± √(-111)
               4

 

x = -(1) ± 10.54
              4

 

x = -(1) + 10.54
              4

or

x = -(1) - 10.54
              4

 

x = 9. 54    or -11.54

        4               4

 

x = 2.39 or - 2.89