Question

What is the value of the expression below when w = 3. 4w^2 - 7w - 8

Answer 1

Answer: w =(-40-√4320)/-34=(20+6√ 30 )/17= 3.110

w =(-40+√4320)/-34=(20-6√ 30 )/17= -0.757

Step-by-step explanation:  The prime factorization of  4320   is

  2•2•2•2•2•3•3•3•5  

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).

√ 4320   =  √ 2•2•2•2•2•3•3•3•5   =2•2•3•√ 30   =

               ±  12 • √ 30

 √ 30   , rounded to 4 decimal digits, is   5.4772

So now we are looking at:

          w  =  ( -40 ± 12 •  5.477 ) / -34

Two real solutions:

w =(-40+√4320)/-34=(20-6√ 30 )/17= -0.757

or:

w =(-40-√4320)/-34=(20+6√ 30 )/17= 3.110

MY HEAD HURTS!