%5E2%3D7.jpeg "(x-3)^2=7")
Solving the Equation (x - 3)^2 = 7
This equation represents a quadratic equation in a slightly disguised form. To solve for x, we need to isolate it. Here's how we can do it:
1. Take the Square Root of Both Sides
The first step is to get rid of the square on the left side. We do this by taking the square root of both sides of the equation:
√((x - 3)^2) = ±√7
Remember that taking the square root of a number results in both positive and negative solutions.
2. Simplify
Simplifying the left side, we get:
x - 3 = ±√7
3. Isolate x
Now, we add 3 to both sides to isolate x:
x = 3 ±√7
4. Solutions
Therefore, the solutions to the equation (x - 3)^2 = 7 are:
x = 3 + √7 and x = 3 - √7
These represent the two points where the graph of the function y = (x - 3)^2 intersects the line y = 7.