Solve 3sqrt{73-3h}=4sqrt{57-7h}

$$3 \sqrt { 73 - 3 h } = 4 \sqrt { 57 - 7 h }$$

Solve for h

$$h=3$$

Solution Steps

Square both sides of the equation.

$$\left(3\sqrt{73-3h}\right)^{2}=\left(4\sqrt{57-7h}\right)^{2}$$

Expand \left(3\sqrt{73-3h}\right)^{2}.

$$3^{2}\left(\sqrt{73-3h}\right)^{2}=\left(4\sqrt{57-7h}\right)^{2}$$

Calculate 3 to the power of 2 and get 9.

$$9\left(\sqrt{73-3h}\right)^{2}=\left(4\sqrt{57-7h}\right)^{2}$$

Calculate \sqrt{73-3h} to the power of 2 and get 73-3h.

$$9\left(73-3h\right)=\left(4\sqrt{57-7h}\right)^{2}$$

Use the distributive property to multiply 9 by 73-3h.

$$657-27h=\left(4\sqrt{57-7h}\right)^{2}$$

Expand \left(4\sqrt{57-7h}\right)^{2}.

$$657-27h=4^{2}\left(\sqrt{57-7h}\right)^{2}$$

Calculate 4 to the power of 2 and get 16.

$$657-27h=16\left(\sqrt{57-7h}\right)^{2}$$

Calculate \sqrt{57-7h} to the power of 2 and get 57-7h.

$$657-27h=16\left(57-7h\right)$$

Use the distributive property to multiply 16 by 57-7h.

$$657-27h=912-112h$$

Add 112h to both sides.

$$657-27h+112h=912$$

Combine -27h and 112h to get 85h.

$$657+85h=912$$

Subtract 657 from both sides.

$$85h=912-657$$

Subtract 657 from 912 to get 255.

$$85h=255$$

Divide both sides by 85.

$$h=\frac{255}{85}$$

Divide 255 by 85 to get 3.

$$h=3$$

Substitute 3 for h in the equation 3\sqrt{73-3h}=4\sqrt{57-7h}.

$$3\sqrt{73-3\times 3}=4\sqrt{57-7\times 3}$$

Simplify. The value h=3 satisfies the equation.

$$24=24$$

Equation 3\sqrt{73-3h}=4\sqrt{57-7h} has a unique solution.

$$h=3$$