(x-9)^2=49

Jasonbradley

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Jun 17, 2024

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Solving the Equation (x-9)² = 49

This article will guide you through solving the equation (x-9)² = 49.

Understanding the Equation

The equation involves a squared term, which means we need to consider both positive and negative solutions.

Solving for x

1. Take the square root of both sides: √((x-9)²) = ±√49

2. Simplify: x - 9 = ±7

3. Isolate x: x = 9 ± 7

4. Calculate both possible solutions:

   • x = 9 + 7 = 16
   • x = 9 - 7 = 2

Solutions

Therefore, the solutions to the equation (x-9)² = 49 are x = 16 and x = 2.

Verification

We can verify our solutions by plugging them back into the original equation:

• For x = 16: (16-9)² = 7² = 49 (correct)
• For x = 2: (2-9)² = (-7)² = 49 (correct)

Both solutions satisfy the original equation.