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Solving the Equation: (x+3)^2 - 5 = 9
This article will guide you through the process of solving the equation (x + 3)² - 5 = 9 step-by-step.
1. Isolating the Squared Term
First, we need to isolate the term containing the squared expression, (x + 3)². To do this, add 5 to both sides of the equation:
(x + 3)² - 5 + 5 = 9 + 5
This simplifies to:
(x + 3)² = 14
2. Taking the Square Root
Now, we take the square root of both sides of the equation. Remember that taking the square root can result in both a positive and a negative value:
√(x + 3)² = ±√14
This gives us:
x + 3 = ±√14
3. Solving for x
Finally, subtract 3 from both sides to isolate x:
x + 3 - 3 = ±√14 - 3
This gives us the two possible solutions for x:
x = √14 - 3
x = -√14 - 3
Conclusion
Therefore, the solutions to the equation (x + 3)² - 5 = 9 are x = √14 - 3 and x = -√14 - 3.