Question

Which of the following sets represents the solution of the equation below?

Answer 1

`x=(-1+√(5)i)/(3)` or
`x=(-√(5)i-1)/(3)`

Explanation:

The given equation is

`-(3)/(2)x^2=x+1`

We multiply through by -2 to get;

`3x^2=-2x-2`

We rewrite in standard quadratic equation form to obtain;

`3x^2+2x+2=0`

The solution to this equation can be found using the formula;

`x=(-b\pm√(b^2-4ac))/(2a)`

where
`a=3,b=2,c=2`

We substitute these values to obtain;

`x=(-2\pm√(2^2-4(3)(2)))/(2(3))`

This implies that;

`x=(-2\pm√(4-24))/(6)`

`x=(-2\pm√(-20))/(6)`

`x=(-2\pm2√(-5))/(6)`

`x=(-1\pm√(5)i)/(3)`

Hence the solution is;

`x=(-1+√(5)i)/(3)` or
`x=(-√(5)i-1)/(3)`