Solve sqrt{28-n}=sqrt{n-8}

$$\sqrt { 28 - n } = \sqrt { n - 8 }$$

Solve for n

$$n=18$$

Solution Steps

Square both sides of the equation.

$$\left(\sqrt{28-n}\right)^{2}=\left(\sqrt{n-8}\right)^{2}$$

Calculate \sqrt{28-n} to the power of 2 and get 28-n.

$$28-n=\left(\sqrt{n-8}\right)^{2}$$

Calculate \sqrt{n-8} to the power of 2 and get n-8.

$$28-n=n-8$$

Subtract n from both sides.

$$28-n-n=-8$$

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

$$28-2n=-8$$

Subtract 28 from both sides.

$$-2n=-8-28$$

Subtract 28 from -8 to get -36.

$$-2n=-36$$

Divide both sides by -2.

$$n=\frac{-36}{-2}$$

Divide -36 by -2 to get 18.

$$n=18$$

Substitute 18 for n in the equation \sqrt{28-n}=\sqrt{n-8}.

$$\sqrt{28-18}=\sqrt{18-8}$$

Simplify. The value n=18 satisfies the equation.

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

Equation \sqrt{28-n}=\sqrt{n-8} has a unique solution.

$$n=18$$