(x-7)^2=60 Square Root

Jasonbradley

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Jun 17, 2024

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Solving the Equation (x-7)^2 = 60

This article will guide you through solving the equation (x-7)^2 = 60 by using the square root property.

Understanding the Square Root Property

The square root property states that if a² = b, then a = ±√b. This property allows us to isolate the variable by taking the square root of both sides of the equation.

Solving the Equation

1. Take the square root of both sides: Applying the square root property, we get: √[(x-7)²] = ±√60

2. Simplify the square roots: The square root of (x-7)² is simply (x-7), and we can simplify √60 as √(4*15) = 2√15. Therefore, we have: x - 7 = ±2√15

3. Isolate x: Add 7 to both sides of the equation: x = 7 ± 2√15

4. The Solutions: This gives us two solutions:

   • x = 7 + 2√15
   • x = 7 - 2√15

Conclusion

By applying the square root property and simplifying the equation, we have successfully solved for x in the equation (x-7)² = 60. The solutions are x = 7 + 2√15 and x = 7 - 2√15.