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Solving the Equation: (x-5)^2 + 5 = 49
This article will guide you through solving the equation (x-5)² + 5 = 49. We will break down the process step by step, ensuring you understand each stage.
Step 1: Isolate the Squared Term
First, we need to isolate the term (x-5)². To do this, subtract 5 from both sides of the equation:
(x-5)² + 5 - 5 = 49 - 5
This simplifies to:
(x-5)² = 44
Step 2: Take the Square Root of Both Sides
Now, take the square root of both sides of the equation to get rid of the square:
√(x-5)² = ±√44
This simplifies to:
(x-5) = ±√44
Step 3: Simplify the Square Root
The square root of 44 can be simplified:
√44 = √(4 * 11) = 2√11
Therefore, we have:
(x-5) = ±2√11
Step 4: Solve for x
Finally, isolate 'x' by adding 5 to both sides of the equation:
x - 5 + 5 = ±2√11 + 5
This gives us the two possible solutions:
x = 5 + 2√11
x = 5 - 2√11
Conclusion
By following these steps, we successfully solved the equation (x-5)² + 5 = 49 and found two possible solutions for 'x'. Remember to always check your answers by plugging them back into the original equation to verify their validity.