Please help me factor this.

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Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...

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)

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.

2x^{2} + x - 14

Using the quadratic formula;

x = -b ± √ (b^{2} - 4ac)

2a

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

x = -(1) ± √ ((1)^{2} - 4(2)(14))

2(2)

2(2)

x = -(1) ± √ (1 - 112)

4

4

x = -(1) ± √(-111)

4

4

x = -(1) ± 10.54

4

4

x = -(1) + 10.54

4

4

or

x = -(1) - 10.54

4

4

x = 9. 54 or -11.54

4 4

x = 2.39 or - 2.89

Hi Ebenezer

2X^2 + X -14

b^2 - 4 ac = 1^2 - 4 ( 2) ( -14) = 1 +112 = 113

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## Comments

^{2}- 4*2*(-14)) )