(x-5)^2=17

Jasonbradley

2 min read

·

Jun 17, 2024

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Solving the Equation (x-5)^2 = 17

This equation presents a quadratic equation in a slightly disguised form. Let's break down how to solve it:

Understanding the Equation

The equation (x-5)^2 = 17 essentially says: "What number, when decreased by 5 and then squared, equals 17?"

Steps to Solve

1. Isolate the squared term:
   To isolate (x-5)^2, we don't need to do anything in this case. It is already isolated.

2. Take the square root of both sides: √[(x-5)^2] = ±√17 This gives us: x - 5 = ±√17

3. Solve for x: x = 5 ±√17

Final Solution

Therefore, the solutions to the equation (x-5)^2 = 17 are:

• x = 5 + √17
• x = 5 - √17

Conclusion

By understanding the structure of the equation and applying basic algebraic operations, we can solve for the unknown variable. This approach can be applied to other quadratic equations in various forms.