Solve (3/sqrt{18}-sqrt{72}):sqrt{50}=k

$$( \frac { 3 } { \sqrt { 18 } } - \sqrt { 72 } ) : \sqrt { 50 } = k$$

Solve for k

$$k = -\frac{11}{10} = -1\frac{1}{10} = -1.1$$

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}.

$$\frac{\frac{3}{3\sqrt{2}}-\sqrt{72}}{\sqrt{50}}=k$$

Rationalize the denominator of \frac{3}{3\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\frac{3\sqrt{2}}{3\left(\sqrt{2}\right)^{2}}-\sqrt{72}}{\sqrt{50}}=k$$

The square of \sqrt{2} is 2.

$$\frac{\frac{3\sqrt{2}}{3\times 2}-\sqrt{72}}{\sqrt{50}}=k$$

Cancel out 3 in both numerator and denominator.

$$\frac{\frac{\sqrt{2}}{2}-\sqrt{72}}{\sqrt{50}}=k$$

Factor 72=6^{2}\times 2. Rewrite the square root of the product \sqrt{6^{2}\times 2} as the product of square roots \sqrt{6^{2}}\sqrt{2}. Take the square root of 6^{2}.

$$\frac{\frac{\sqrt{2}}{2}-6\sqrt{2}}{\sqrt{50}}=k$$

Combine \frac{\sqrt{2}}{2} and -6\sqrt{2} to get -\frac{11}{2}\sqrt{2}.

$$\frac{-\frac{11}{2}\sqrt{2}}{\sqrt{50}}=k$$

Factor 50=5^{2}\times 2. Rewrite the square root of the product \sqrt{5^{2}\times 2} as the product of square roots \sqrt{5^{2}}\sqrt{2}. Take the square root of 5^{2}.

$$\frac{-\frac{11}{2}\sqrt{2}}{5\sqrt{2}}=k$$

Cancel out \sqrt{2} in both numerator and denominator.

$$\frac{-\frac{11}{2}}{5}=k$$

Express \frac{-\frac{11}{2}}{5} as a single fraction.

$$\frac{-11}{2\times 5}=k$$

Multiply 2 and 5 to get 10.

$$\frac{-11}{10}=k$$

Fraction \frac{-11}{10} can be rewritten as -\frac{11}{10} by extracting the negative sign.

$$-\frac{11}{10}=k$$

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

$$k=-\frac{11}{10}$$