%5E2%3D0.jpeg "(x+7)^2=0")
Solving the Equation (x+7)² = 0
This equation presents a simple quadratic equation, but understanding its solution can be insightful. Let's break down the steps:
Understanding the Equation
- (x+7)² represents the square of the expression (x+7). This means the expression is multiplied by itself: (x+7) * (x+7).
- = 0 indicates that the result of the squared expression must equal zero.
Solving for x
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Square Root Property: To get rid of the square, we take the square root of both sides of the equation: √(x+7)² = √0
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Simplifying: This simplifies to: x + 7 = 0
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Isolate x: Subtract 7 from both sides: x = -7
Conclusion
Therefore, the solution to the equation (x+7)² = 0 is x = -7. This solution signifies that the expression (x+7) is equal to zero when x is -7.
Insights
- Double Root: This equation has a double root, meaning the solution x = -7 appears twice. This is because the square of any number (positive or negative) is always positive, except for zero.
- Graphing: The graph of the function y = (x+7)² is a parabola that intersects the x-axis at the point (-7, 0). This point represents the double root.
Understanding the solution of this simple quadratic equation helps build a foundation for solving more complex equations in algebra and other areas of mathematics.