Solve x=-ksqrt{1-x^2}

$$x = - k \sqrt { 1 - x ^ { 2 } }$$

Solve for k

$$k=-\frac{x}{\sqrt{1-x^{2}}}$$

$$|x|<1$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$\left(-k\right)\sqrt{1-x^{2}}=x$$

Reorder the terms.

$$-k\sqrt{-x^{2}+1}=x$$

The equation is in standard form.

$$\left(-\sqrt{1-x^{2}}\right)k=x$$

Divide both sides by -\sqrt{-x^{2}+1}.

$$\frac{\left(-\sqrt{1-x^{2}}\right)k}{-\sqrt{1-x^{2}}}=\frac{x}{-\sqrt{1-x^{2}}}$$

Dividing by -\sqrt{-x^{2}+1} undoes the multiplication by -\sqrt{-x^{2}+1}.

$$k=\frac{x}{-\sqrt{1-x^{2}}}$$

Divide x by -\sqrt{-x^{2}+1}.

$$k=-\frac{x}{\sqrt{1-x^{2}}}$$

Solve for x

$$x=-\frac{k}{\sqrt{k^{2}+1}}$$