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# factor 2x^2+x-14

### 3 Answers by Expert Tutors

Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...
4.8 4.8 (4 lesson ratings) (4)
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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)
David T. | Experienced Math and Physics TutorExperienced Math and Physics Tutor
4.8 4.8 (12 lesson ratings) (12)
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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.

To extend my solution, we have:

(1/4) * (-1 ± √(12- 4*2*(-14)) )

= (1/4) * (-1 ± √(1 + 112) )

= (1/4) * (-1 ± √(113) )

= -1/4 ± √(113)/4 = x

which is irrational. So, using this knowledge and our knowledge of the leading coefficient being 2, we have the solution:

(leading coefficient)*(first zero)*(second zero)

or

2*(x + 1/4 + √(113)/4)*(x + 1/4 - √(113)/4)

I believe that Parviz failed to properly evaluate in his last two steps, which I believe is just a error in the parenthesis placement, an easy mistake when typing. Ebenezer evaluated 2x^2 + x + 14, demonstrating how much a slight change can effect a solution.
Ebenezer O. | Aerospace Engr & Air Traffic Control Grad For General Ed. TutoringAerospace Engr & Air Traffic Control Gra...
4.6 4.6 (13 lesson ratings) (13)
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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