Solve for x

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

multipy both sides by x^2

-x^2=x+1
now solve it.
0=x^2+x+1
which is not easily solved
Using the quadratic formula

x=(-1+- sqrt(1-4))/2 but notice the sqrt is a sqrt(-3), which is an imaginary number, so your roots are complex, not real.

multiply each term by x^2, which is the LCM

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

use the quadratic equation to find the two complex roots.

To solve for x in the equation -1 = 1/x + 1/(x^2), we need to find a common denominator for the two fractions on the right side of the equation.

First, let's rewrite the equation with a common denominator of x^2:

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

Next, multiply both sides of the equation by x^2 to eliminate the denominator:

-1 * x^2 = x + x^2

Simplifying further, we have:

-x^2 = x + x^2

Combine like terms by moving x^2 to the left side:

0 = 2x^2 + x

Now, we have a quadratic equation. To solve for x, we can rearrange the equation:

2x^2 + x = 0

Factor out the common term x:

x(2x + 1) = 0

From here, we can use the zero product property, which states that if a product of two terms is equal to zero, then at least one of the terms must be zero.

Setting each factor equal to zero:

x = 0
2x + 1 = 0

Solving the second equation:

2x = -1
x = -1/2

Therefore, the two solutions for x are x = 0 and x = -1/2.