Solve ax^2-2ax+a+1=0

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

Solve for a

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

$$x\neq 1$$

Steps for Solving Linear Equation

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

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

Combine all terms containing a.

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

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

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

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

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

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

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

Solve for x (complex solution)

$$x=\frac{a+\sqrt{-a}}{a}$$

$$x=\frac{a-\sqrt{-a}}{a}\text{, }a\neq 0$$

Solve for x

$$x=\frac{a+\sqrt{-a}}{a}$$

$$x=\frac{a-\sqrt{-a}}{a}\text{, }a<0$$