(b+7)^2=0

2 min read Jun 16, 2024
(b+7)^2=0

Solving the Equation (b + 7)^2 = 0

This equation presents a simple yet effective example of solving a quadratic equation. Let's break it down step-by-step.

Understanding the Equation

The equation (b + 7)^2 = 0 represents a perfect square trinomial. This means the expression on the left side is the result of squaring a binomial.

Solving for b

  1. Take the square root of both sides: √((b + 7)^2) = √(0) This simplifies to: b + 7 = 0

  2. Isolate b: Subtract 7 from both sides: b + 7 - 7 = 0 - 7 This leaves us with: b = -7

The Solution

Therefore, the solution to the equation (b + 7)^2 = 0 is b = -7.

Key Points

  • Unique Solution: This quadratic equation has only one solution. This is because the equation represents a perfect square, and the square of any number (except zero) is always positive.
  • Graphical Interpretation: The graph of the function y = (b + 7)^2 is a parabola that touches the x-axis at the point (-7, 0). This point represents the solution to the equation.

Conclusion

Solving the equation (b + 7)^2 = 0 demonstrates a fundamental concept in algebra - finding the roots of a quadratic equation. By utilizing the properties of perfect squares and basic algebraic manipulations, we can efficiently arrive at the solution.

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