Question

How do you solve `x^2-2x-2=0`?

Answer 1

Use the quadratic formula to get
`color(white)("XXXX")` `x= 1+-sqrt(3)`

Explanation:

For any quadratic equation of the form
`color(white)("XXXX")` `ax^2+bx+c=0`
the solutions are given by the formula
`color(white)("XXXX")` `x= (-b+-sqrt(b^2-4ac))/(2a)`

Given `x^2-2x-2=0`
`a=1` `color(white)("XXXX")` `b=-2` `color(white)("XXXX")` `c=-2`
and the quadratic formula gives
`color(white)("XXXX")` `x= (2+-sqrt((-2)^2-4(1)(-2)))/(2(1))`

`color(white)("XXXX")` `color(white)("XXXX")` `= (2+-sqrt(12))/2`

`color(white)("XXXX")` `color(white)("XXXX")` `=(2+-2sqrt(3))/2`

`color(white)("XXXX")` `color(white)("XXXX")` `=1+-sqrt(3)`