Question

factorisation of 8x^2 +16x-51
$8x { }^{2 } + 16x - 51$
​

Answer 1

Answer:

x =(-16-√1888)/16=-1-1/4√ 118 = -3.716

x =(-16+√1888)/16=-1+1/4√ 118 = 1.716

Step-by-step explanation:

According to the Quadratic Formula,  x, the solution for   Ax2+Bx+C  = 0  , where  A, B, and  C  are numbers, often called coefficients, is given by :

                                     

           - B  ±  √ B2-4AC

 x =   ————————

                     2A

 In our case,  A   =     8

                     B   =    16

                     C   =  -51

Accordingly,  B2  -  4AC   =

                    256 - (-1632) =

                    1888

Applying the quadratic formula :

              -16 ± √ 1888

  x  =    ———————

                       16

Can  √ 1888 be simplified ?

Yes!   The prime factorization of  1888   is

  2•2•2•2•2•59  

To be able to remove something from under the radical, there have to be  2  instances of it (because we are taking a square i.e. second root).

√ 1888   =  √ 2•2•2•2•2•59   =2•2•√ 118   =

               ±  4 • √ 118

 √ 118, rounded to 4 decimal digits, is  10.8628

So now we are looking at:

          x  =  ( -16 ± 4 •  10.863 ) / 16

Two real solutions:

x =(-16+√1888)/16=-1+1/4√ 118 = 1.716

or:

x =(-16-√1888)/16=-1-1/4√ 118 = -3.716

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