(x+5)^4=16

Jasonbradley

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Jun 17, 2024

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Solving the Equation (x+5)^4 = 16

This equation involves a fourth power, which might seem intimidating at first, but we can solve it systematically. Here's how:

1. Isolate the Term with the Variable

Start by taking the fourth root of both sides of the equation:

(x+5)^4 = 16 (x+5) = ±√[4]16 (x+5) = ±2

We get two possible solutions because the fourth root of a number can be positive or negative.

2. Solve for x

Now, we have two separate equations to solve:

• x + 5 = 2
• x + 5 = -2

Solving for x in each equation:

• x = -3
• x = -7

Conclusion

Therefore, the solutions to the equation (x+5)^4 = 16 are x = -3 and x = -7.