Solve 5(x/2+1/5)=-1/2+sqrt{5}

$$5( \frac{ x }{ 2 } + \frac{ 1 }{ 5 } )= \frac{ -1 }{ 2 } + \sqrt{ 5 }$$

Solve for x

$$x=\frac{2\sqrt{5}-3}{5}\approx 0.294427191$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 10, the least common multiple of 2,5.

$$50\left(\frac{x}{2}+\frac{1}{5}\right)=5\left(-1\right)+10\sqrt{5}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 5 is 10. Multiply \frac{x}{2} times \frac{5}{5}. Multiply \frac{1}{5} times \frac{2}{2}.

$$50\left(\frac{5x}{10}+\frac{2}{10}\right)=5\left(-1\right)+10\sqrt{5}$$

Since \frac{5x}{10} and \frac{2}{10} have the same denominator, add them by adding their numerators.

$$50\times \frac{5x+2}{10}=5\left(-1\right)+10\sqrt{5}$$

Cancel out 10, the greatest common factor in 50 and 10.

$$5\left(5x+2\right)=5\left(-1\right)+10\sqrt{5}$$

Use the distributive property to multiply 5 by 5x+2.

$$25x+10=5\left(-1\right)+10\sqrt{5}$$

Multiply 5 and -1 to get -5.

$$25x+10=-5+10\sqrt{5}$$

Subtract 10 from both sides.

$$25x=-5+10\sqrt{5}-10$$

Subtract 10 from -5 to get -15.

$$25x=-15+10\sqrt{5}$$

The equation is in standard form.

$$25x=10\sqrt{5}-15$$

Divide both sides by 25.

$$\frac{25x}{25}=\frac{10\sqrt{5}-15}{25}$$

Dividing by 25 undoes the multiplication by 25.

$$x=\frac{10\sqrt{5}-15}{25}$$

Divide -15+10\sqrt{5} by 25.

$$x=\frac{2\sqrt{5}-3}{5}$$