Question

How do you solve `x^2 - 6x - 3 = 0`?

Answer 1

`x = 3+-2sqrt(3)`

Explanation:

Complete the square then use the difference of squares identity:

`a^2-b^2=(a-b)(a+b)`

with `a=(x-3)` and `b=2sqrt(3)` as follows:

`0 = x^2-6x-3`

`color(white)(0) = x^2-6x+9-12`

`color(white)(0) = (x-3)^2-(2sqrt(3))^2`

`color(white)(0) = ((x-3)-2sqrt(3))((x-3)+2sqrt(3))`

`color(white)(0) = (x-3-2sqrt(3))(x-3+2sqrt(3))`

Hence:

`x = 3+-2sqrt(3)`