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(x+1)^2=25

2 min read Jun 16, 2024
(x+1)^2=25

Solving the Equation (x + 1)² = 25

This equation is a simple quadratic equation that we can solve using a few methods. Here's how:

Method 1: Taking the Square Root

  1. Isolate the squared term: Since the right side is already a constant, we don't need to do anything here.

  2. Take the square root of both sides: √(x + 1)² = ±√25

  3. Simplify: x + 1 = ±5

  4. Solve for x:

    • x + 1 = 5 => x = 4
    • x + 1 = -5 => x = -6

Therefore, the solutions to the equation (x + 1)² = 25 are x = 4 and x = -6.

Method 2: Expanding and Solving

  1. Expand the left side: x² + 2x + 1 = 25

  2. Move all terms to one side: x² + 2x - 24 = 0

  3. Factor the quadratic: (x + 6)(x - 4) = 0

  4. Set each factor equal to zero:

    • x + 6 = 0 => x = -6
    • x - 4 = 0 => x = 4

Again, the solutions are x = 4 and x = -6.

Conclusion

Both methods lead to the same solutions. The first method is simpler and faster if you're comfortable with square roots. The second method is useful for understanding the relationship between quadratic equations and factoring.

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