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Solving Equations Using the Square Root Property: (x + 3)² = 16
The square root property is a powerful tool for solving quadratic equations, especially those that can be written in the form of a squared term equal to a constant. Let's explore how to use this property to solve the equation (x + 3)² = 16.
Understanding the Square Root Property
The square root property states that if a² = b, then a = ±√b. This means that if we have a squared term equal to a constant, we can take the square root of both sides to isolate the variable. Remember, we need to consider both positive and negative square roots.
Applying the Property to Solve (x + 3)² = 16
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Take the square root of both sides: √(x + 3)² = ±√16
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Simplify: x + 3 = ±4
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Isolate x: x = -3 ± 4
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Solve for both possibilities:
- x = -3 + 4 = 1
- x = -3 - 4 = -7
Conclusion
Therefore, the solutions to the equation (x + 3)² = 16 are x = 1 and x = -7. By applying the square root property, we successfully isolated the variable and found two distinct solutions. Remember to always consider both positive and negative square roots when using this property.