Solve the equation `x^(2)-10x-2=0` by the method of completing the square.

Explanation

We have
`x^(2)-10x-2=0`
`implies" "x^(2)-10x=0`
`implies" "x^(2)-2xx x xx5+5^(2)=2+5^(2)" "["adding "5^(2)" on both sides"]`
`implies" "(x-5)^(2)=(2+25)=27`
`implies" "x-5=+-sqrt(27)=+-3sqrt(3)" "["taking square root on both sides"]`
`implies" "x-5=3sqrt(3)" or "x-5=-3sqrt(3)`
`implies" "x=(5+3sqrt(3))" or "x=(5-3sqrt(3)).`
Hence, `(5+3sqrt(3))` and `(5-3sqrt(3))` are the roots of the given equation.