Question

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

Answer 1

`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`