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.