What are solutions of 3x2+14x+16=0?p

x =(14-√388)/6=(7-√ 97 )/3= -0.950

 x =(14+√388)/6=(7+√ 97 )/3= 5.616

explanation: Equation at the end of step  1  :

(3x2 - 14x) - 16 = 0

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  3x2-14x-16

Equation at the end of step  2  :

3x2 - 14x - 16 = 0

Step  3  :

Parabola, Finding the Vertex :

 3.1      Find the Vertex of   y = 3x2-14x-16

Add  7/3  to both sides to obtain:

   x = 7/3 + √ 97/9

Since a square root has two values, one positive and the other negative

   x2 - (14/3)x - (16/3) = 0

   has two solutions:

  x = 7/3 + √ 97/9

   or

  x = 7/3 - √ 97/9

Note that  √ 97/9 can be written as

  √ 97  / √ 9   which is √ 97  / 3

Solve Quadratic Equation using the Quadratic Formula

 3.3     Solving    3x2-14x-16 = 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   =     3

                      B   =   -14

                      C   =  -16

Accordingly,  B2  -  4AC   =

                     196 - (-192) =

                     388

Applying the quadratic formula :

               14 ± √ 388

   x  =    ——————

                      6

Can  √ 388 be simplified ?

Yes!   The prime factorization of  388   is

   2•2•97 

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).

√ 388   =  √ 2•2•97   =

                ±  2 • √ 97

10% of increase is the final answer! : )