Solve x^2+10b^2-6ab-2b+1=0

$$x ^ { 2 } + 10 b ^ { 2 } - 6 a b - 2 b + 1 = 0$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=\frac{x^{2}+10b^{2}-2b+1}{6b}\text{, }&b\neq 0\\a\in \mathrm{C}\text{, }&\left(x=i\text{ or }x=-i\right)\text{ and }b=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$10b^{2}-6ab-2b+1=-x^{2}$$

Subtract 10b^{2} from both sides.

$$-6ab-2b+1=-x^{2}-10b^{2}$$

Add 2b to both sides.

$$-6ab+1=-x^{2}-10b^{2}+2b$$

Subtract 1 from both sides.

$$-6ab=-x^{2}-10b^{2}+2b-1$$

The equation is in standard form.

$$\left(-6b\right)a=-x^{2}-10b^{2}+2b-1$$

Divide both sides by -6b.

$$\frac{\left(-6b\right)a}{-6b}=\frac{-x^{2}-10b^{2}+2b-1}{-6b}$$

Dividing by -6b undoes the multiplication by -6b.

$$a=\frac{-x^{2}-10b^{2}+2b-1}{-6b}$$

Divide 2b-1-x^{2}-10b^{2} by -6b.

$$a=\frac{x^{2}+1}{6b}+\frac{5b}{3}-\frac{1}{3}$$

Solve for a

$$a=\frac{x^{2}+10b^{2}-2b+1}{6b}$$

$$b\neq 0$$

Steps for Solving Linear Equation

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

$$10b^{2}-6ab-2b+1=-x^{2}$$

Subtract 10b^{2} from both sides.

$$-6ab-2b+1=-x^{2}-10b^{2}$$

Add 2b to both sides.

$$-6ab+1=-x^{2}-10b^{2}+2b$$

Subtract 1 from both sides.

$$-6ab=-x^{2}-10b^{2}+2b-1$$

The equation is in standard form.

$$\left(-6b\right)a=-x^{2}-10b^{2}+2b-1$$

Divide both sides by -6b.

$$\frac{\left(-6b\right)a}{-6b}=\frac{-x^{2}-10b^{2}+2b-1}{-6b}$$

Dividing by -6b undoes the multiplication by -6b.

$$a=\frac{-x^{2}-10b^{2}+2b-1}{-6b}$$

Divide -x^{2}-10b^{2}+2b-1 by -6b.

$$a=\frac{x^{2}+1}{6b}+\frac{5b}{3}-\frac{1}{3}$$

Solve for b (complex solution)

$$b=\frac{\sqrt{-10x^{2}+9a^{2}+6a-9}+3a+1}{10}$$

$$b=\frac{-\sqrt{-10x^{2}+9a^{2}+6a-9}+3a+1}{10}$$

Solve for b

$$b=\frac{\sqrt{-10x^{2}+9a^{2}+6a-9}+3a+1}{10}$$

$$b=\frac{-\sqrt{-10x^{2}+9a^{2}+6a-9}+3a+1}{10}\text{, }\left(a\leq \frac{-\sqrt{10}-1}{3}\text{ or }a\geq \frac{\sqrt{10}-1}{3}\right)\text{ and }|x|\leq \frac{\sqrt{90a^{2}+60a-90}}{10}$$