Solve x4+4x3-19x2+14x=0

$$x4+4x3-19x2+14x=0$$

Solve for x

$$x=\frac{19x_{2}}{14}-\frac{x_{4}}{14}-\frac{2x_{3}}{7}$$

Steps for Solving Linear Equation

Subtract x_{4} from both sides. Anything subtracted from zero gives its negation.

$$4x_{3}-19x_{2}+14x=-x_{4}$$

Subtract 4x_{3} from both sides.

$$-19x_{2}+14x=-x_{4}-4x_{3}$$

Add 19x_{2} to both sides.

$$14x=-x_{4}-4x_{3}+19x_{2}$$

The equation is in standard form.

$$14x=19x_{2}-4x_{3}-x_{4}$$

Divide both sides by 14.

$$\frac{14x}{14}=\frac{19x_{2}-4x_{3}-x_{4}}{14}$$

Dividing by 14 undoes the multiplication by 14.

$$x=\frac{19x_{2}-4x_{3}-x_{4}}{14}$$

Divide -x_{4}-4x_{3}+19x_{2} by 14.

$$x=\frac{19x_{2}}{14}-\frac{x_{4}}{14}-\frac{2x_{3}}{7}$$

Solve for x_2

$$x_{2}=\frac{14x+4x_{3}+x_{4}}{19}$$

Steps for Solving Linear Equation

Subtract x_{4} from both sides. Anything subtracted from zero gives its negation.

$$4x_{3}-19x_{2}+14x=-x_{4}$$

Subtract 4x_{3} from both sides.

$$-19x_{2}+14x=-x_{4}-4x_{3}$$

Subtract 14x from both sides.

$$-19x_{2}=-x_{4}-4x_{3}-14x$$

The equation is in standard form.

$$-19x_{2}=-14x-4x_{3}-x_{4}$$

Divide both sides by -19.

$$\frac{-19x_{2}}{-19}=\frac{-14x-4x_{3}-x_{4}}{-19}$$

Dividing by -19 undoes the multiplication by -19.

$$x_{2}=\frac{-14x-4x_{3}-x_{4}}{-19}$$

Divide -x_{4}-4x_{3}-14x by -19.

$$x_{2}=\frac{14x+4x_{3}+x_{4}}{19}$$