Question

Using the quadratic formula to solve 2x2 = 4x – 7, what are the values of x

Answer 1

First you must rewrite the given equation in standard form:

2x^2 - 4x + 7 = 0.  Here a=2, b=-4 and c=7.

The solutions are thus 
       -[-4] plus or minus sqrt( [-4]^2 - 4[2][7] )
x = --------------------------------------------------------
                                   4
                   4 plus or minus sqrt (16 - 56)
or:     x = --------------------------------------------
                                        4

16-56 = - 40, a negative number.  Thus, we must introduce the imaginary operator:  sqrt (-40) = 2i*sqrt(10)

The roots are thus:
         4 plus or minus 2i sqrt(10)              2 plus or minus i*sqrt(10)
x = -----------------------------------------  =  ---------------------------------------
                            4                                                        2