Solve frac{2+sqrt{20}}{2}quadb=frac{1sqrt{2}}{sqrt{2}*5}

$$\frac { 2 + \sqrt { 20 } } { 2 } \quad b = \frac { 1 \sqrt { 2 } } { \sqrt { 2 } \cdot 5 }$$

Solve for b

$$b=\frac{\sqrt{5}-1}{20}\approx 0.061803399$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$\left(2+\sqrt{20}\right)b=\frac{1}{5}\times 2^{\frac{1}{2}}\times 1\sqrt{2}$$

Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.

$$\left(2+2\sqrt{5}\right)b=\frac{1}{5}\times 2^{\frac{1}{2}}\times 1\sqrt{2}$$

Use the distributive property to multiply 2+2\sqrt{5} by b.

$$2b+2\sqrt{5}b=\frac{1}{5}\times 2^{\frac{1}{2}}\times 1\sqrt{2}$$

Multiply \frac{1}{5} and 1 to get \frac{1}{5}.

$$2b+2\sqrt{5}b=\frac{1}{5}\times 2^{\frac{1}{2}}\sqrt{2}$$

Reorder the terms.

$$2\sqrt{5}b+2b=\frac{1}{5}\sqrt{2}\sqrt{2}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$2\sqrt{5}b+2b=\frac{1}{5}\times 2$$

Multiply \frac{1}{5} and 2 to get \frac{2}{5}.

$$2\sqrt{5}b+2b=\frac{2}{5}$$

Combine all terms containing b.

$$\left(2\sqrt{5}+2\right)b=\frac{2}{5}$$

Divide both sides by 2\sqrt{5}+2.

$$\frac{\left(2\sqrt{5}+2\right)b}{2\sqrt{5}+2}=\frac{\frac{2}{5}}{2\sqrt{5}+2}$$

Dividing by 2\sqrt{5}+2 undoes the multiplication by 2\sqrt{5}+2.

$$b=\frac{\frac{2}{5}}{2\sqrt{5}+2}$$

Divide \frac{2}{5} by 2\sqrt{5}+2.

$$b=\frac{\sqrt{5}-1}{20}$$