Question

Solve the equation 3x^2-2x-10=0

Answer 1

Answer:

Step-by-step explanation:

                                 

           - B  ±  √ B2-4AC

 x =   ————————

                     2A

 In our case,  A   =     3

                     B   =    -2

                     C   =  -10

 B2  -  4AC   =

       4 - (-120) =

             =  124

Applying the quadratic formula :

              2 ± √ 124

  x  =    —————

                   6

 √ 124 simplified

 The prime factorization of  124   is

  2•2•31

To be able to remove something from under the radical, there have to be  2  instances of it

√ 124   =  √ 2•2•31   =

               ±  2 • √ 31

 √ 31, rounded to 4 decimal digits, is   5.5678

So now we are looking at:

          x  =  ( 2 ± 2 •  5.568 ) / 6

Two real solutions:

x =(2+√124)/6=(1+√ 31 )/3= 2.189

or:

x =(2-√124)/6=(1-√ 31 )/3= -1.523

Answer 2

Answer:

Step-by-step explanation:

3x^2-2x-10=0

This is a quadratic equation that can be solved using the quadratic formula where

a = 3, b = -2, and c = -10

x=−b±(b^2−4ac)^(1/2)/2a

x=−(−2)±((−2)2−4(3)(−10)^(1/2)/2(3))

x=2±(124)^(1/2)/6

Simplify the Radical:

x=((2/6) ±2(31)^(1/2))/6

x=26±231−−√6

Simplify fractions and/or signs:

x=1/3±√31/3

which becomes

x=2.18925

See the attached image for a more clear display of solving using the quadratic equation.

x=−1.52259