Question

solve:5x^2-2x-8=0,and give your answer correct to 2 decimal places

Answer 1

 Solving    5x2-2x-8 = 0 by the Quadratic Formula :

 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   =     5
                      B   =    -2
                      C   =   -8 

Accordingly,  B2  -  4AC   =
                     4 - (-160) =
                     164

Applying the quadratic formula :

               2 ± √ 164 
   x  =    —————
                    10

Yes!   The prime factorization of  164   is
   2•2•41  
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).

√ 164   =  √ 2•2•41   =
                ±  2 • √ 41 

  √ 41   , rounded to 4 decimal digits, is   6.4031
 So now we are looking at:
           x  =  ( 2 ± 2 •  6.403 ) / 10

Two real solutions:

 x =(2+√164)/10=(1+√ 41 )/5= 1.481 

or:

 x =(2-√164)/10=(1-√ 41 )/5= -1.081 

Two solutions were found :

 x =(2-√164)/10=(1-√ 41 )/5= -1.08
 x =(2+√164)/10=(1+√ 41 )/5= 1.48

Hope it helps.

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