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Solving the Equation (x-3)^2=9
In this article, we will explore the solution to the equation (x-3)^2=9.
Understanding the Equation
The given equation is a quadratic equation of the form (x-a)^2=b, where a=3 and b=9. To solve for x, we need to isolate the variable x.
Step 1: Simplify the Equation
We can start by simplifying the equation by taking the square root of both sides:
(x-3)^2 = 9 x-3 = ±√9 x-3 = ±3
Step 2: Solve for x
Now, we can add 3 to both sides of the equation to get:
x = 3 ± 3
This gives us two possible solutions for x:
x = 3 + 3 = 6 x = 3 - 3 = 0
Therefore, the solutions to the equation (x-3)^2=9 are x=6 and x=0.
Conclusion
In this article, we have solved the equation (x-3)^2=9 and found two solutions: x=6 and x=0. This demonstrates the steps involved in solving a quadratic equation of the form (x-a)^2=b.
