Solve xsqrt{7}=xsqrt{2}+4sqrt{2}

$$x \sqrt { 7 } = x \sqrt { 2 } + 4 \sqrt { 2 }$$

Solve for x

$$x = \frac{4 {(\sqrt{14} + 2)}}{5} \approx 4.593325909$$

Steps for Solving Linear Equation

Subtract x\sqrt{2} from both sides.

$$x\sqrt{7}-x\sqrt{2}=4\sqrt{2}$$

Reorder the terms.

$$\sqrt{7}x-\sqrt{2}x=4\sqrt{2}$$

Combine all terms containing x.

$$\left(\sqrt{7}-\sqrt{2}\right)x=4\sqrt{2}$$

Divide both sides by \sqrt{7}-\sqrt{2}.

$$\frac{\left(\sqrt{7}-\sqrt{2}\right)x}{\sqrt{7}-\sqrt{2}}=\frac{4\sqrt{2}}{\sqrt{7}-\sqrt{2}}$$

Dividing by \sqrt{7}-\sqrt{2} undoes the multiplication by \sqrt{7}-\sqrt{2}.

$$x=\frac{4\sqrt{2}}{\sqrt{7}-\sqrt{2}}$$

Divide 4\sqrt{2} by \sqrt{7}-\sqrt{2}.

$$x=\frac{4\sqrt{14}+8}{5}$$