Solve sqrt{2}+x-4=-sqrt{10}-3x

$$\sqrt { 2 } + x - 4 = - \sqrt { 10 } - 3 x$$

Solve for x

$$x=-\frac{\sqrt{2}}{4}-\frac{\sqrt{10}}{4}+1\approx -0.144122806$$

Steps for Solving Linear Equation

Add 3x to both sides.

$$\sqrt{2}+x-4+3x=-\sqrt{10}$$

Combine x and 3x to get 4x.

$$\sqrt{2}+4x-4=-\sqrt{10}$$

Subtract \sqrt{2} from both sides.

$$4x-4=-\sqrt{10}-\sqrt{2}$$

Add 4 to both sides.

$$4x=-\sqrt{10}-\sqrt{2}+4$$

The equation is in standard form.

$$4x=4-\sqrt{2}-\sqrt{10}$$

Divide both sides by 4.

$$\frac{4x}{4}=\frac{4-\sqrt{2}-\sqrt{10}}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$x=\frac{4-\sqrt{2}-\sqrt{10}}{4}$$

Divide -\sqrt{10}-\sqrt{2}+4 by 4.

$$x=-\frac{\sqrt{2}}{4}-\frac{\sqrt{10}}{4}+1$$