(x+5)^2=9

Jasonbradley

2 min read

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Jun 17, 2024

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Solving the Equation (x + 5)² = 9

This article will walk through the steps to solve the equation (x + 5)² = 9. We'll explore the concepts of squaring, square roots, and how to handle equations with squared terms.

Understanding the Equation

The equation (x + 5)² = 9 involves squaring a binomial (x + 5). This means we're multiplying the entire expression (x + 5) by itself. To solve this, we'll need to work backwards and use the concept of square roots.

Solving for x

1. Take the square root of both sides: Since the left side is squared, we can take the square root of both sides of the equation. Remember that the square root of a number can be both positive and negative.

   √(x + 5)² = ±√9

2. Simplify: The square root of (x + 5)² is simply (x + 5), and the square root of 9 is 3. Therefore, we have:

   x + 5 = ±3

3. Isolate x: To isolate x, subtract 5 from both sides:

   x = ±3 - 5

4. Solve for both possible values of x:

   • x = 3 - 5 = -2
   • x = -3 - 5 = -8

Conclusion

Therefore, the solutions to the equation (x + 5)² = 9 are x = -2 and x = -8.

Remember, always check your answers by plugging them back into the original equation to ensure they are valid solutions.