Question

A number plus twice its reciprocal is negative nineteen-thirds​

Answer 1

The number could be
`x=-6` or
`x=-1/3`

Explanation:

Let

x-----> the number

Remember that

The reciprocal of a number is 1 divided by the number

we know that

`x+2((1)/(x))=-(19)/(3)`

Solve for x

Multiply by 3x both sides

`3x^(2) +6=-19x\\ \\ 3x^(2)+19x+6=0`

Solve the quadratic equation by graphing

The solutions are
`x=-6, x=-1/3`

see the attached figure

Verify both solutions

For
`x=-6`

`-6+2(-(1)/(6))=-(19)/(3)`

`-(19)/(3)=-(19)/(3)` ----> is true

For
`x=-1/3`

`-(1/3)+2((1)/((-1/3)))=-(19)/(3)`

`-(19)/(3)=-(19)/(3)` ----> is true