Solve sqrt{6}+3sqrt{3}x+2x=3sqrt{18}

$$\sqrt{ 6 } +3 \sqrt{ 3 } x+2x=3 \sqrt{ 18 }$$

Solve for x (complex solution)

$$x = \frac{29 \sqrt{6} - 9 \sqrt{2} - 18 \sqrt{2}}{23} \approx 1.42832332$$

Steps for Solving Linear Equation

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$\sqrt{6}+3\sqrt{3}x+2x=3\times 3\sqrt{2}$$

Multiply 3 and 3 to get 9.

$$\sqrt{6}+3\sqrt{3}x+2x=9\sqrt{2}$$

Subtract \sqrt{6} from both sides.

$$3\sqrt{3}x+2x=9\sqrt{2}-\sqrt{6}$$

Combine all terms containing x.

$$\left(3\sqrt{3}+2\right)x=9\sqrt{2}-\sqrt{6}$$

Divide both sides by 3\sqrt{3}+2.

$$\frac{\left(3\sqrt{3}+2\right)x}{3\sqrt{3}+2}=\frac{9\sqrt{2}-\sqrt{6}}{3\sqrt{3}+2}$$

Dividing by 3\sqrt{3}+2 undoes the multiplication by 3\sqrt{3}+2.

$$x=\frac{9\sqrt{2}-\sqrt{6}}{3\sqrt{3}+2}$$

Divide 9\sqrt{2}-\sqrt{6} by 3\sqrt{3}+2.

$$x=\frac{29\sqrt{6}-27\sqrt{2}}{23}$$

Solve for x

$$x = \frac{29 \sqrt{6} - 27 \sqrt{2}}{23} \approx 1.42832332$$

Steps for Solving Linear Equation

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$\sqrt{6}+3\sqrt{3}x+2x=3\times 3\sqrt{2}$$

Multiply 3 and 3 to get 9.

$$\sqrt{6}+3\sqrt{3}x+2x=9\sqrt{2}$$

Subtract \sqrt{6} from both sides.

$$3\sqrt{3}x+2x=9\sqrt{2}-\sqrt{6}$$

Combine all terms containing x.

$$\left(3\sqrt{3}+2\right)x=9\sqrt{2}-\sqrt{6}$$

Divide both sides by 3\sqrt{3}+2.

$$\frac{\left(3\sqrt{3}+2\right)x}{3\sqrt{3}+2}=\frac{9\sqrt{2}-\sqrt{6}}{3\sqrt{3}+2}$$

Dividing by 3\sqrt{3}+2 undoes the multiplication by 3\sqrt{3}+2.

$$x=\frac{9\sqrt{2}-\sqrt{6}}{3\sqrt{3}+2}$$

Divide 9\sqrt{2}-\sqrt{6} by 3\sqrt{3}+2.

$$x=\frac{29\sqrt{6}-27\sqrt{2}}{23}$$