Answer:
[tex]x=\sqrt{v^2 -\frac{2k}{m}}[/tex]
Explanation:
Equation Solving
The procedure to solve an equation consists in trying to isolate the required variable by applying algebra and / or elemental properties of some functions. If not possible, then we could use formulas or iterative approaches.
The equation to solve is
[tex]\displaystyle k=\frac{1}{2}mv^2 -\frac{1}{2} mx^2[/tex]
Rearranging
[tex]\displaystyle \frac{1}{2} mx^2=\frac{1}{2}mv^2 -k[/tex]
Multiplying by 2/m
[tex]\displaystyle x^2=v^2 -\frac{2k}{m}[/tex]
Solving for x
[tex]\displaystyle \boxed{x=\sqrt{v^2 -\frac{2k}{m}}}[/tex]
