Solve sqrt{15-n}=sqrt{3n-33}

$$\sqrt{ 15-n } = \sqrt{ 3n-33 }$$

Solve for n

$$n=12$$

Solution Steps

Square both sides of the equation.

$$\left(\sqrt{15-n}\right)^{2}=\left(\sqrt{3n-33}\right)^{2}$$

Calculate \sqrt{15-n} to the power of 2 and get 15-n.

$$15-n=\left(\sqrt{3n-33}\right)^{2}$$

Calculate \sqrt{3n-33} to the power of 2 and get 3n-33.

$$15-n=3n-33$$

Subtract 3n from both sides.

$$15-n-3n=-33$$

Combine -n and -3n to get -4n.

$$15-4n=-33$$

Subtract 15 from both sides.

$$-4n=-33-15$$

Subtract 15 from -33 to get -48.

$$-4n=-48$$

Divide both sides by -4.

$$n=\frac{-48}{-4}$$

Divide -48 by -4 to get 12.

$$n=12$$

Substitute 12 for n in the equation \sqrt{15-n}=\sqrt{3n-33}.

$$\sqrt{15-12}=\sqrt{3\times 12-33}$$

Simplify. The value n=12 satisfies the equation.

$$3^{\frac{1}{2}}=3^{\frac{1}{2}}$$

Equation \sqrt{15-n}=\sqrt{3n-33} has a unique solution.

$$n=12$$