Solve 5x/sqrt{5}=5-x

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

Solve for x

$$x = \frac{5 {(\sqrt{5} - 1)}}{4} \approx 1.545084972$$

Steps for Solving Linear Equation

Rationalize the denominator of \frac{5x}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{5x\sqrt{5}}{\left(\sqrt{5}\right)^{2}}=5-x$$

The square of \sqrt{5} is 5.

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

Cancel out 5 and 5.

$$x\sqrt{5}=5-x$$

Add x to both sides.

$$x\sqrt{5}+x=5$$

Combine all terms containing x.

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

Divide both sides by \sqrt{5}+1.

$$\frac{\left(\sqrt{5}+1\right)x}{\sqrt{5}+1}=\frac{5}{\sqrt{5}+1}$$

Dividing by \sqrt{5}+1 undoes the multiplication by \sqrt{5}+1.

$$x=\frac{5}{\sqrt{5}+1}$$

Divide 5 by \sqrt{5}+1.

$$x=\frac{5\sqrt{5}-5}{4}$$