Solve sqrt{3k-29}=sqrt{41-2k}

$$\sqrt { 3 k - 29 } = \sqrt { 41 - 2 k }$$

Solve for k

$$k=14$$

Solution Steps

Square both sides of the equation.

$$\left(\sqrt{3k-29}\right)^{2}=\left(\sqrt{41-2k}\right)^{2}$$

Calculate \sqrt{3k-29} to the power of 2 and get 3k-29.

$$3k-29=\left(\sqrt{41-2k}\right)^{2}$$

Calculate \sqrt{41-2k} to the power of 2 and get 41-2k.

$$3k-29=41-2k$$

Add 2k to both sides.

$$3k-29+2k=41$$

Combine 3k and 2k to get 5k.

$$5k-29=41$$

Add 29 to both sides.

$$5k=41+29$$

Add 41 and 29 to get 70.

$$5k=70$$

Divide both sides by 5.

$$k=\frac{70}{5}$$

Divide 70 by 5 to get 14.

$$k=14$$

Substitute 14 for k in the equation \sqrt{3k-29}=\sqrt{41-2k}.

$$\sqrt{3\times 14-29}=\sqrt{41-2\times 14}$$

Simplify. The value k=14 satisfies the equation.

$$13^{\frac{1}{2}}=13^{\frac{1}{2}}$$

Equation \sqrt{3k-29}=\sqrt{41-2k} has a unique solution.

$$k=14$$