Can you explain and solve for x.

`x^2+x-18=0`

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Solve `x^2+x-18=0` :

The quadratic expression does not factor in the rationals (no rational factors of 18 are 1 unit apart.) So we can use other methods:

(1) If `ax^2+bx+c=0` then the quadratic formula is

`x=(-b+-sqrt(b^2-4ac))/(2a)`

Here a=1,b=1,c=-18:

So `x=(-1+-sqrt(1^2-4(1)(-18)))/(2(1))`

`=(-1+-sqrt(73))/2`

`=-1/2+sqrt(73)/2` or `-1/2-sqrt(73)/2`

(2) We can use completing the square:

`x^2+x-18=0`

`x^2+x=18`

`x^2+x+1/4=18+1/4`

`(x+1/2)^2=73/4`

`x+1/2=+-sqrt(73/4)`

`x=-1/2+-sqrt(73)/2` as before.

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