Question

How do you solve `x^2 - 2x - 18 = 0` using the quadratic formula?

Answer 1

`x= 1+sqrt(19)` or `x=1-sqrt(19)`
(see below for solution using the quadratic formula)

Explanation:

The quadratic formula says that for any quadratic in the form:
`color(white)("XXXX")` `ax^2+bx+c=0`
the roots (solution) can be determined by:
`color(white)("XXXX")` `x= (-b+-sqrt(b^2-4ac))/(2a)`

For the given equation `x^2-2x-18=0`
`a=1` `color(white)("XXXX")` `b=-2` `color(white)("XXXX")` `c=-18`

So the solutions are
`color(white)("XXXX")` `x=(2+-sqrt((-2)^2-4(1)(-18)))/(2(1))`

`color(white)("XXXX")` `color(white)("XXXX")` `= (2+-sqrt(4+72))/2`

`color(white)("XXXX")` `color(white)("XXXX")` `=(2+-sqrt(76))/2`

`color(white)("XXXX")` `color(white)("XXXX")` `=(2+-2sqrt(19))/2`

`color(white)("XXXX")` `color(white)("XXXX")` `= 1+-sqrt(19)`