%5E2%2F5%3D9.jpeg "(x-7)^2/5=9")
Solving the Equation: (x-7)^2/5 = 9
This article will guide you through the steps to solve the equation (x-7)^2/5 = 9.
Understanding the Equation
The equation involves a few key elements:
- Parentheses: The expression (x-7) is enclosed in parentheses, indicating that we need to perform the operations inside them first.
- Exponent: The term (x-7) is squared, meaning it is multiplied by itself.
- Division: The entire squared term is divided by 5.
- Equality: The equation uses the equals sign, meaning the left side must equal the right side.
Step-by-Step Solution
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Multiply both sides by 5: (x-7)^2 = 45
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Take the square root of both sides: x - 7 = ±√45
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Simplify the square root: x - 7 = ±3√5
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Add 7 to both sides: x = 7 ± 3√5
Solutions
The equation has two solutions:
- x = 7 + 3√5
- x = 7 - 3√5
Conclusion
The solutions to the equation (x-7)^2/5 = 9 are x = 7 + 3√5 and x = 7 - 3√5. By carefully applying the rules of algebra and simplifying the expression, we arrive at the solutions.