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