Solve x^2-2a(x-1)-1=0

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

Solve for a (complex solution)

$$\left\{\begin{matrix}\\a=\frac{x+1}{2}\text{, }&\text{unconditionally}\\a\in \mathrm{C}\text{, }&x=1\end{matrix}\right.$$

Steps for Solving Linear Equation

Add 1 to both sides. Anything plus zero gives itself.

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

Use the distributive property to multiply -2a by x-1.

$$x^{2}-2ax+2a=1$$

Subtract x^{2} from both sides.

$$-2ax+2a=1-x^{2}$$

Combine all terms containing a.

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

The equation is in standard form.

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

Divide both sides by -2x+2.

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

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

$$a=\frac{1-x^{2}}{2-2x}$$

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

$$a=\frac{x+1}{2}$$

Solve for a

$$\left\{\begin{matrix}\\a=\frac{x+1}{2}\text{, }&\text{unconditionally}\\a\in \mathrm{R}\text{, }&x=1\end{matrix}\right.$$

Steps for Solving Linear Equation

Add 1 to both sides. Anything plus zero gives itself.

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

Use the distributive property to multiply -2a by x-1.

$$x^{2}-2ax+2a=1$$

Subtract x^{2} from both sides.

$$-2ax+2a=1-x^{2}$$

Combine all terms containing a.

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

The equation is in standard form.

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

Divide both sides by -2x+2.

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

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

$$a=\frac{1-x^{2}}{2-2x}$$

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

$$a=\frac{x+1}{2}$$

Solve for x

$$x=2a-1$$

$$x=1$$