Solve sqrt{20-2n}=sqrt{n+5}

$$\sqrt { 20 - 2 n } = \sqrt { n + 5 }$$

Solve for n

$$n=5$$

Solution Steps

Square both sides of the equation.

$$\left(\sqrt{20-2n}\right)^{2}=\left(\sqrt{n+5}\right)^{2}$$

Calculate \sqrt{20-2n} to the power of 2 and get 20-2n.

$$20-2n=\left(\sqrt{n+5}\right)^{2}$$

Calculate \sqrt{n+5} to the power of 2 and get n+5.

$$20-2n=n+5$$

Subtract n from both sides.

$$20-2n-n=5$$

Combine -2n and -n to get -3n.

$$20-3n=5$$

Subtract 20 from both sides.

$$-3n=5-20$$

Subtract 20 from 5 to get -15.

$$-3n=-15$$

Divide both sides by -3.

$$n=\frac{-15}{-3}$$

Divide -15 by -3 to get 5.

$$n=5$$

Substitute 5 for n in the equation \sqrt{20-2n}=\sqrt{n+5}.

$$\sqrt{20-2\times 5}=\sqrt{5+5}$$

Simplify. The value n=5 satisfies the equation.

$$10^{\frac{1}{2}}=10^{\frac{1}{2}}$$

Equation \sqrt{20-2n}=\sqrt{n+5} has a unique solution.

$$n=5$$