K=1/2kx^2 solve for the variable x

To solve the equation K = (1/2)kx^2 for the variable x, we will follow the steps below:

Step 1: Understand the equation.
- The equation relates K (a constant), k (a constant), and x (the variable we want to solve for).
- The equation represents a relationship between potential energy (K), the stiffness of the spring (k), and the displacement from equilibrium (x).

Step 2: Isolate the variable.
- Multiply both sides of the equation by 2 to eliminate the fraction:
2K = kx^2

Step 3: Divide both sides by k.
- Divide both sides of the equation by k to isolate x^2:
(2K) / k = (kx^2) / k
2K/k = x^2

Step 4: Take the square root of both sides.
- Find the square root of both sides of the equation to solve for x:
√(2K/k) = √(x^2)

Step 5: Simplify the equation.
- The square root of x^2 simplifies to |x|, where the absolute value represents both the positive and negative roots.
√(2K/k) = |x|

Therefore, the variable x can be expressed as:
x = ± √(2K/k)

Make sure to include the ± symbol, as there are two possible values for x due to the absolute value.