Solve H^8-2(3x+1)=x

$$H ^ { 8 } - 2 ( 3 x + 1 ) = x$$

Solve for x

$$x=\frac{H^{8}-2}{7}$$

Steps for Solving Linear Equation

Use the distributive property to multiply -2 by 3x+1.

$$H^{8}-6x-2=x$$

Subtract x from both sides.

$$H^{8}-6x-2-x=0$$

Combine -6x and -x to get -7x.

$$H^{8}-7x-2=0$$

Subtract H^{8} from both sides. Anything subtracted from zero gives its negation.

$$-7x-2=-H^{8}$$

Add 2 to both sides.

$$-7x=-H^{8}+2$$

The equation is in standard form.

$$-7x=2-H^{8}$$

Divide both sides by -7.

$$\frac{-7x}{-7}=\frac{2-H^{8}}{-7}$$

Dividing by -7 undoes the multiplication by -7.

$$x=\frac{2-H^{8}}{-7}$$

Divide -H^{8}+2 by -7.

$$x=\frac{H^{8}-2}{7}$$

Solve for H (complex solution)

$$H\in \sqrt{2}\left(\frac{1}{2}+\frac{1}{2}i\right)\sqrt[8]{7x+2},\sqrt[8]{7x+2},i\sqrt[8]{7x+2},\sqrt{2}\left(-\frac{1}{2}+\frac{1}{2}i\right)\sqrt[8]{7x+2},-\sqrt[8]{7x+2},\sqrt{2}\left(-\frac{1}{2}-\frac{1}{2}i\right)\sqrt[8]{7x+2},-i\sqrt[8]{7x+2},\sqrt{2}\left(\frac{1}{2}-\frac{1}{2}i\right)\sqrt[8]{7x+2}$$

Solve for H

$$H=\sqrt[8]{7x+2}$$

$$H=-\sqrt[8]{7x+2}\text{, }x\geq -\frac{2}{7}$$