Find the solution(s) to each of these equations, or explain why there is no solution.

1. \(\sqrt{x+5}+7 = 10\)
2. \(\sqrt{x-2}+3=\text-2\)

For each equation, decide how many solutions it has and explain how you know.

1. \((x-4)^2= 25\)
2. \(\sqrt{x-4} = 5\)<
3. \(x^3 -7 = \text-20\)
4. \(6 \boldcdot \sqrt[3]{x} = 0\)

The volume of a regular tetrahedron (a pyramid made from 4 equilateral triangles) with side length \(s\) is given by the formula \(V = \frac{1}{6\sqrt{2}} \boldcdot s^3\). 

1. Solve this equation for \(s\) to get the side length in terms of the volume.

2. If the volume of a regular tetrahedron is \(18\sqrt{2}\) cubic centimeters, what is the length of one of the sides of the tetrahedron?