2-%3D-17.jpeg "(x – 5)2 = 17")
Solving the Equation (x – 5)2 = 17
This equation involves a squared term and a constant, making it a quadratic equation. Here's how to solve for the values of x:
1. Isolate the Squared Term
Begin by taking the square root of both sides of the equation:
√[(x – 5)2] = ±√17
This gives us:
x – 5 = ±√17
2. Solve for x
Now, isolate x by adding 5 to both sides:
x = 5 ±√17
3. Finding the Solutions
Therefore, the solutions to the equation (x – 5)2 = 17 are:
- x = 5 + √17
- x = 5 – √17
These are the two distinct values of x that satisfy the original equation.
Understanding the Result
This equation represents a parabola with its vertex at (5, 0). The solutions we found are the x-coordinates where the parabola intersects the horizontal line y = √17.