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Solving the Equation (x+1)² = 16
This article will guide you through solving the equation (x+1)² = 16. We will explore the steps involved in finding the solutions and discuss the concept behind the equation.
Understanding the Equation
The equation (x+1)² = 16 represents a quadratic equation. A quadratic equation is an equation with a highest power of 2 for the variable. In this case, the variable is 'x'.
Solving for x
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Take the square root of both sides: To eliminate the square, we take the square root of both sides of the equation. Remember that taking the square root results in both a positive and negative solution.
√(x+1)² = ±√16
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Simplify: This simplifies to: x+1 = ±4
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Solve for x: We now have two separate equations to solve:
- x+1 = 4
- x+1 = -4
Solving the first equation: x = 4 - 1 x = 3
Solving the second equation: x = -4 - 1 x = -5
Solutions
Therefore, the solutions to the equation (x+1)² = 16 are:
- x = 3
- x = -5
Conclusion
By understanding the concept of quadratic equations and following the steps outlined above, we successfully solved the equation (x+1)² = 16 and found its two solutions. This process can be applied to solve similar quadratic equations in various mathematical contexts.