Question

What is the solution set of the equation `x^2+sqrt2x=1/2`?

Answer 1

`x=-1/sqrt2+1` or `-1/sqrt2-1`

Explanation:

`x^2+sqrt2x=1/2` can be written as

`2x^2+2sqrt2x-1=0`

Hence using quadratic formula

`x=(-2sqrt2+-sqrt((2sqrt2)^2-4xx2xx(-1)))/(2xx2)`

`=(-2sqrt2+-sqrt(8+8))/4`

`=-sqrt2/2+-4/4`

`=-1/sqrt2+-1`

i.e `-1/sqrt2+1` or `-1/sqrt2-1`