(x+6)^3=28

2 min read Jun 17, 2024

Solving the Equation (x+6)^3 = 28

This equation presents a cubic equation that we need to solve for the value of 'x'. Here's a step-by-step approach to find the solution:

1. Isolate the Cube:

Begin by taking the cube root of both sides of the equation:
```
∛[(x+6)^3] = ∛28
```
This simplifies to:
```
x + 6 = ∛28
```

2. Isolate 'x':

Subtract 6 from both sides of the equation:
```
x + 6 - 6 = ∛28 - 6
```
This leaves us with:
```
x = ∛28 - 6
```

3. Approximating the Solution:

The cube root of 28 is not a whole number. We can approximate it using a calculator to get a decimal representation:
```
x ≈ 3.036 - 6
```
Therefore, the approximate solution for 'x' is:
```
x ≈ -2.964
```

Conclusion:

The equation (x+6)^3 = 28 has one real solution, which is approximately x ≈ -2.964. It's important to remember that cubic equations can have up to three real solutions. In this case, the other two solutions are complex numbers.