Solve for k
k=-x-1-\frac{1}{x}
x\neq 0
Solve for x (complex solution)
x=\frac{\sqrt{\left(k-1\right)\left(k+3\right)}-k-1}{2}
x=\frac{-\sqrt{\left(k-1\right)\left(k+3\right)}-k-1}{2}
Solve for x
x=\frac{\sqrt{\left(k-1\right)\left(k+3\right)}-k-1}{2}
x=\frac{-\sqrt{\left(k-1\right)\left(k+3\right)}-k-1}{2}\text{, }k\leq -3\text{ or }k\geq 1
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kx+1=-x-x^{2}
Subtract x^{2} from both sides.
kx=-x-x^{2}-1
Subtract 1 from both sides.
xk=-x^{2}-x-1
The equation is in standard form.
\frac{xk}{x}=\frac{-x^{2}-x-1}{x}
Divide both sides by x.
k=\frac{-x^{2}-x-1}{x}
Dividing by x undoes the multiplication by x.
k=-x-1-\frac{1}{x}
Divide -x-x^{2}-1 by x.
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