Solve 5+2sqrt{5}=p+xsqrt{5}

$$5+2 \sqrt{ 5 } = p+x \sqrt{ 5 }$$

Solve for x

$$x=-\frac{\sqrt{5}p}{5}+\sqrt{5}+2$$

Steps for Solving Linear Equation

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

$$p+x\sqrt{5}=5+2\sqrt{5}$$

Subtract p from both sides.

$$x\sqrt{5}=5+2\sqrt{5}-p$$

The equation is in standard form.

$$\sqrt{5}x=-p+2\sqrt{5}+5$$

Divide both sides by \sqrt{5}.

$$\frac{\sqrt{5}x}{\sqrt{5}}=\frac{-p+2\sqrt{5}+5}{\sqrt{5}}$$

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

$$x=\frac{-p+2\sqrt{5}+5}{\sqrt{5}}$$

Divide 5+2\sqrt{5}-p by \sqrt{5}.

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

Solve for p

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