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Solving the Equation (x+5)² = 25
This article will guide you through solving the equation (x+5)² = 25. We will use the concept of square roots and algebraic manipulations to find the possible values of x.
Understanding the Equation
The equation (x+5)² = 25 represents a quadratic equation. It tells us that the square of the expression (x+5) is equal to 25. To solve for x, we need to find the values that satisfy this equation.
Solving for x
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Take the square root of both sides: Since the left side is squared, we can take the square root of both sides to get rid of the square. Remember that the square root of a number has both positive and negative solutions.
√(x+5)² = ±√25
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Simplify: This simplifies to:
x + 5 = ±5
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Isolate x: Subtract 5 from both sides:
x = ±5 - 5
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Solve for both solutions:
- For the positive solution: x = 5 - 5 = 0
- For the negative solution: x = -5 - 5 = -10
The Solution
Therefore, the solutions to the equation (x+5)² = 25 are x = 0 and x = -10.
Verification
We can verify our solutions by plugging them back into the original equation:
- For x = 0: (0 + 5)² = 5² = 25
- For x = -10: (-10 + 5)² = (-5)² = 25
Both solutions satisfy the original equation.
Conclusion
By understanding the properties of square roots and using algebraic manipulation, we successfully solved the equation (x+5)² = 25, finding the solutions x = 0 and x = -10. This process illustrates how to approach quadratic equations and find their solutions.