(x+4)^2=49

3 min read Jun 16, 2024

Solving the Equation (x + 4)^2 = 49

This article will guide you through solving the equation (x + 4)^2 = 49. We will use the concept of square roots to find the solutions for x.

Understanding the Equation

The equation represents a quadratic equation, which means it involves a variable raised to the power of two. To solve for x, we need to isolate it.

Solving for x

Take the square root of both sides: To get rid of the square on the left side, we take the square root of both sides of the equation:
```
√(x + 4)² = ±√49
```
Simplify: The square root of a squared term is simply the term itself. The square root of 49 is 7. Remember, we need to consider both positive and negative square roots. This gives us:
```
x + 4 = ±7
```
Solve for x: Now we have two separate equations:
- x + 4 = 7
- x + 4 = -7
Solve each equation:
- x = 7 - 4 = 3
- x = -7 - 4 = -11

Solutions

Therefore, the solutions to the equation (x + 4)² = 49 are x = 3 and x = -11.

Verification

To verify our solutions, we can substitute each value of x back into the original equation:

For x = 3: (3 + 4)² = 7² = 49. This is correct.
For x = -11: (-11 + 4)² = (-7)² = 49. This is also correct.

Conclusion

We have successfully solved the equation (x + 4)² = 49 using the square root property. We found two solutions: x = 3 and x = -11. This process demonstrates how to solve quadratic equations involving squares.