%5E2%2B5%3D15.jpeg "(x-3)^2+5=15")
Solving the Equation: (x-3)^2 + 5 = 15
This article will guide you through solving the equation (x-3)^2 + 5 = 15. We will break down the steps and explain the reasoning behind each one.
Step 1: Isolate the Squared Term
Our goal is to get the term (x-3)^2 by itself on one side of the equation. To do this, subtract 5 from both sides:
(x-3)^2 + 5 - 5 = 15 - 5
This simplifies to:
(x-3)^2 = 10
Step 2: Take the Square Root of Both Sides
To eliminate the square on the left side, take the square root of both sides of the equation:
√(x-3)^2 = ±√10
Remember to include both the positive and negative square roots.
Step 3: Solve for x
The square root of a squared term is simply the term itself. Therefore, we have:
(x-3) = ±√10
Now, isolate 'x' by adding 3 to both sides:
x = 3 ±√10
Step 4: Express the Solutions
This gives us two possible solutions for 'x':
- x = 3 + √10
- x = 3 - √10
Conclusion
We have successfully solved the equation (x-3)^2 + 5 = 15, and found two solutions: x = 3 + √10 and x = 3 - √10.
By following these steps, you can solve similar equations involving squared terms. Remember to always isolate the squared term, take the square root of both sides, and consider both positive and negative solutions.