How do you find the roots, real and imaginary, of #y=(2x-8)(x-2)-x^2-x # using the quadratic formula?

1 Answer
Dec 6, 2015

Answer:

#x~= 13.844 or x~= 1.156#

Explanation:

Step 1: Multiply/FOIL the expression

#y= (2x-8)(x-2)-x^2 -x#
#y = 2x^2 -4x -8x + 16-x^2 -x#
#y = x^2 -15x + 16#

Step 2: Set the equation equal to zero
#0= x^2 -15x + 16#

Quadratic formula
#x= (-b+-sqrt(b^2-4ac))/2a#

#a= 1 , b = -15, c= 16#

Substitute into the formula

#x = (-(-15) +- sqrt((-15)^2 -4(1)(16)))/2#

#x = (15 +- sqrt(225 -64))/2#

#x= (15 +sqrt(161))/2#

#x= (15+-(12.688577))/2#

#x = (15+12.688577)/2 = 13.844288# or

#x= (15- 12.688577)/2 = 1.1557115#