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

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

Solve for x

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

$$a\neq 0$$

Steps for Solving Linear Equation

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

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

Subtract 1 from both sides.

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

The equation is in standard form.

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

Divide both sides by -2a.

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

Dividing by -2a undoes the multiplication by -2a.

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

Divide -a^{2}-1 by -2a.

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

Solve for a (complex solution)

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

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

Solve for a

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

$$a=-\sqrt{x^{2}-1}+x\text{, }|x|\geq 1$$