Solve kx^2+2kx+1=0

$$k x ^ { 2 } + 2 k x + 1 = 0$$

Solve for k

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

$$x\neq -2\text{ and }x\neq 0$$

Steps for Solving Linear Equation

Subtract 1 from both sides. Anything subtracted from zero gives its negation.

$$kx^{2}+2kx=-1$$

Combine all terms containing k.

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

Divide both sides by x^{2}+2x.

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

Dividing by x^{2}+2x undoes the multiplication by x^{2}+2x.

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

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

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

Solve for x (complex solution)

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

$$x=-\frac{\sqrt{k\left(k-1\right)}+k}{k}\text{, }k\neq 0$$

Solve for x

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

$$x=-\frac{\sqrt{k\left(k-1\right)}+k}{k}\text{, }k<0\text{ or }k\geq 1$$