Question

How do you solve `x^2-10x-9=0`?

Answer 1

`x = 5+-sqrt(34)`

Explanation:

The difference of squares identity can be written:

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

Use this with `a = (x-5)` and `b=sqrt(34)` as follows:

`0 = x^2-10x-9`

`color(white)(0) = x^2-10x+25-34`

`color(white)(0) = (x-5)^2-(sqrt(34))^2`

`color(white)(0) = ((x-5)-sqrt(34))((x-5)+sqrt(34))`

`color(white)(0) = (x-5-sqrt(34))(x-5+sqrt(34))`

Hence `x = 5+-sqrt(34)`