Solve x=sqrt{2}x+15x+5

$$x = \sqrt{ 2 } x+15x+5$$

Solve for x

$$x=\frac{5\left(\sqrt{2}-14\right)}{194}\approx -0.324375939$$

Steps for Solving Linear Equation

Subtract \sqrt{2}x from both sides.

$$x-\sqrt{2}x=15x+5$$

Subtract 15x from both sides.

$$x-\sqrt{2}x-15x=5$$

Combine x and -15x to get -14x.

$$-14x-\sqrt{2}x=5$$

Combine all terms containing x.

$$\left(-14-\sqrt{2}\right)x=5$$

The equation is in standard form.

$$\left(-\sqrt{2}-14\right)x=5$$

Divide both sides by -14-\sqrt{2}.

$$\frac{\left(-\sqrt{2}-14\right)x}{-\sqrt{2}-14}=\frac{5}{-\sqrt{2}-14}$$

Dividing by -14-\sqrt{2} undoes the multiplication by -14-\sqrt{2}.

$$x=\frac{5}{-\sqrt{2}-14}$$

Divide 5 by -14-\sqrt{2}.

$$x=\frac{5\sqrt{2}}{194}-\frac{35}{97}$$