A linear
spring has a potential energy of 7.3 J when it is stretched 0.29 m.
What is the constant for this spring?
spring potential energy: Us = 7.3 J
displacement: x = 0.29 m
Starting formula 

Algebra: multiply each side by 2 

Algebra: 2's cancel on right 

Algebra: divide each side by x^2 

Algebra: x^2's cancel on right 

Algebra: switch left and right 

Plug in numbers with units 

Multiply: (2)(7.3)/0.29^2 = 173.602.... 

Final result with significant figures and unit 