%5E2%3D49.jpeg "(x+5)^2=49")
Solving the Equation (x+5)^2 = 49
This equation involves a squared term, which means we'll need to use the square root property to solve for x. Here's how:
1. Take the square root of both sides:
√(x+5)² = ±√49
Remember: When taking the square root of both sides of an equation, we need to consider both the positive and negative square roots.
2. Simplify:
x + 5 = ±7
3. Isolate x:
x = -5 ±7
4. Solve for both possible solutions:
- x = -5 + 7 = 2
- x = -5 - 7 = -12
Therefore, the solutions to the equation (x+5)² = 49 are x = 2 and x = -12.
Checking the Solutions
We can check our solutions by plugging them back into the original equation:
- For x = 2:
- (2+5)² = 7² = 49 (True)
- For x = -12:
- (-12+5)² = (-7)² = 49 (True)
Both solutions satisfy the original equation, confirming our answers are correct.