A linear
spring has a potential energy of 25 J and a constant of 510 N/m. How
far has it been stretched?
spring potential energy: Us = 25 J
spring constant: k = 510 N/m
Starting formula 

Algebra: multiply each side by 2 

Algebra: 2's cancel on right 

Algebra: divide each side by k 

Algebra: k's cancel on right 

Algebra: take square root of each side 

Algebra: square root of x^2 is x 

Algebra: switch left and right 

Plug in numbers with units 

Math: sqrt(2(25)/510) = 0.313.... 

Final result with significant figures and unit 