%5E2%3D25%2F36.jpeg "(x-8)^2=25/36")
Solving the Equation: (x-8)^2 = 25/36
This equation involves a squared term, making it a quadratic equation. Here's how to solve it:
1. Take the Square Root of Both Sides
To isolate the term (x-8), we need to get rid of the square. This can be done by taking the square root of both sides of the equation:
√[(x-8)^2] = ±√(25/36)
Remember that taking the square root introduces both positive and negative solutions.
2. Simplify
Simplify both sides of the equation:
x - 8 = ±(5/6)
3. Isolate x
To find the value of x, add 8 to both sides:
x = 8 ± (5/6)
4. Find the Two Solutions
This gives us two possible solutions:
- x = 8 + (5/6) = 53/6
- x = 8 - (5/6) = 43/6
Conclusion
Therefore, the solutions to the equation (x-8)^2 = 25/36 are x = 53/6 and x = 43/6.