(x+5)^2=25

3 min read Jun 17, 2024
(x+5)^2=25

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

  1. 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

  2. Simplify: This simplifies to:

    x + 5 = ±5

  3. Isolate x: Subtract 5 from both sides:

    x = ±5 - 5

  4. 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.

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