Solve 7x^2+2kx+k+1=0

$$7 x ^ { 2 } + 2 k x + k + 1 = 0$$

Solve for k

$$k=-\frac{7x^{2}+1}{2x+1}$$

$$x\neq -\frac{1}{2}$$

Steps for Solving Linear Equation

Subtract 7x^{2} from both sides. Anything subtracted from zero gives its negation.

$$2kx+k+1=-7x^{2}$$

Subtract 1 from both sides.

$$2kx+k=-7x^{2}-1$$

Combine all terms containing k.

$$\left(2x+1\right)k=-7x^{2}-1$$

Divide both sides by 2x+1.

$$\frac{\left(2x+1\right)k}{2x+1}=\frac{-7x^{2}-1}{2x+1}$$

Dividing by 2x+1 undoes the multiplication by 2x+1.

$$k=\frac{-7x^{2}-1}{2x+1}$$

Divide -7x^{2}-1 by 2x+1.

$$k=-\frac{7x^{2}+1}{2x+1}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{k^{2}-7k-7}-k}{7}$$

$$x=\frac{-\sqrt{k^{2}-7k-7}-k}{7}$$

Solve for x

$$x=\frac{\sqrt{k^{2}-7k-7}-k}{7}$$

$$x=\frac{-\sqrt{k^{2}-7k-7}-k}{7}\text{, }k\geq \frac{\sqrt{77}+7}{2}\text{ or }k\leq \frac{7-\sqrt{77}}{2}$$