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 stepbystep.
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

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

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 xaxis 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.