(x+5)^2=49

2 min read Jun 17, 2024
(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.

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