Solve sqrt{21}(sqrt{3}x+2sqrt{21})=5

$$\sqrt { 21 } ( \sqrt { 3 } x + 2 \sqrt { 21 } ) = 5$$

Solve for x

$$x = -\frac{37 \sqrt{7}}{21} \approx -4.661561834$$

Steps for Solving Linear Equation

Use the distributive property to multiply \sqrt{21} by \sqrt{3}x+2\sqrt{21}.

$$\sqrt{21}\sqrt{3}x+2\left(\sqrt{21}\right)^{2}=5$$

Factor 21=3\times 7. Rewrite the square root of the product \sqrt{3\times 7} as the product of square roots \sqrt{3}\sqrt{7}.

$$\sqrt{3}\sqrt{7}\sqrt{3}x+2\left(\sqrt{21}\right)^{2}=5$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$3\sqrt{7}x+2\left(\sqrt{21}\right)^{2}=5$$

The square of \sqrt{21} is 21.

$$3\sqrt{7}x+2\times 21=5$$

Multiply 2 and 21 to get 42.

$$3\sqrt{7}x+42=5$$

Subtract 42 from both sides.

$$3\sqrt{7}x=5-42$$

Subtract 42 from 5 to get -37.

$$3\sqrt{7}x=-37$$

Divide both sides by 3\sqrt{7}.

$$\frac{3\sqrt{7}x}{3\sqrt{7}}=-\frac{37}{3\sqrt{7}}$$

Dividing by 3\sqrt{7} undoes the multiplication by 3\sqrt{7}.

$$x=-\frac{37}{3\sqrt{7}}$$

Divide -37 by 3\sqrt{7}.

$$x=-\frac{37\sqrt{7}}{21}$$