Solve x^2+2x-(k-1)=0

$$x ^ { 2 } + 2 x - ( k - 1 ) = 0$$

Solve for k

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

Steps for Solving Linear Equation

To find the opposite of k-1, find the opposite of each term.

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

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

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

Subtract 2x from both sides.

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

Subtract 1 from both sides.

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

Divide both sides by -1.

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

Dividing by -1 undoes the multiplication by -1.

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

Divide -\left(x+1\right)^{2} by -1.

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

Solve for x (complex solution)

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

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

Solve for x

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

$$x=-\sqrt{k}-1\text{, }k\geq 0$$