(x-1/2)^3=1/27

Jasonbradley

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Jun 17, 2024

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Solving the Equation (x - 1/2)³ = 1/27

This equation involves a cube root and requires us to solve for the value of 'x'. Here's how we can break it down:

1. Take the Cube Root of Both Sides

The first step is to get rid of the cube on the left-hand side of the equation. We can do this by taking the cube root of both sides:

∛[(x - 1/2)³] = ∛(1/27)

This simplifies to:

x - 1/2 = 1/3

2. Isolate the Variable 'x'

To get 'x' by itself, we need to add 1/2 to both sides of the equation:

x - 1/2 + 1/2 = 1/3 + 1/2

This simplifies to:

x = 5/6

Solution

Therefore, the solution to the equation (x - 1/2)³ = 1/27 is x = 5/6.