%5E2%3D12.jpeg "(x-5)^2=12")
Solving the Equation (x - 5)^2 = 12
This equation involves a squared term, making it a quadratic equation. We can solve for x using the following steps:
1. Taking the Square Root of Both Sides
First, we isolate the squared term by taking the square root of both sides of the equation:
√[(x - 5)^2] = ±√12
This gives us:
x - 5 = ±√12
2. Simplifying the Radical
The square root of 12 can be simplified as follows:
√12 = √(4 * 3) = 2√3
3. Isolating x
Now, we can isolate x by adding 5 to both sides of the equation:
x = 5 ± 2√3
4. Finding the Solutions
Therefore, the solutions to the equation (x - 5)^2 = 12 are:
- x = 5 + 2√3
- x = 5 - 2√3
These are the two distinct values of x that satisfy the original equation.