Solve sqrt{98}-sqrt{32}=xsqrt{2}

$$\sqrt{ 98 } - \sqrt{ 32 } =x \sqrt{ 2 }$$

Solve for x

$$x=3$$

Steps for Solving Linear Equation

Factor 98=7^{2}\times 2. Rewrite the square root of the product \sqrt{7^{2}\times 2} as the product of square roots \sqrt{7^{2}}\sqrt{2}. Take the square root of 7^{2}.

$$7\sqrt{2}-\sqrt{32}=x\sqrt{2}$$

Factor 32=4^{2}\times 2. Rewrite the square root of the product \sqrt{4^{2}\times 2} as the product of square roots \sqrt{4^{2}}\sqrt{2}. Take the square root of 4^{2}.

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

Combine 7\sqrt{2} and -4\sqrt{2} to get 3\sqrt{2}.

$$3\sqrt{2}=x\sqrt{2}$$

Swap sides so that all variable terms are on the left hand side.

$$x\sqrt{2}=3\sqrt{2}$$

The equation is in standard form.

$$\sqrt{2}x=3\sqrt{2}$$

Divide both sides by \sqrt{2}.

$$\frac{\sqrt{2}x}{\sqrt{2}}=\frac{3\sqrt{2}}{\sqrt{2}}$$

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

$$x=\frac{3\sqrt{2}}{\sqrt{2}}$$

Divide 3\sqrt{2} by \sqrt{2}.

$$x=3$$