%5E2%3D20.jpeg "(x-5)^2=20")
Solving the Equation (x-5)^2 = 20
This equation involves a squared term, which makes it a quadratic equation. Here's how to solve it:
1. Isolate the Squared Term
The first step is to get the squared term by itself on one side of the equation. In this case, it already is:
(x-5)^2 = 20
2. Take the Square Root of Both Sides
To get rid of the square, we take the square root of both sides of the equation:
√(x-5)^2 = ±√20
Remember to include both positive and negative square roots when taking the square root of a number.
3. Simplify
Simplifying the equation gives us:
x - 5 = ±√20
We can simplify √20 further as 2√5.
x - 5 = ±2√5
4. Isolate x
To get x by itself, add 5 to both sides of the equation:
x = 5 ± 2√5
5. Solutions
Therefore, the two solutions to the equation (x-5)^2 = 20 are:
- x = 5 + 2√5
- x = 5 - 2√5
These are the exact solutions. You can also approximate them to decimal form using a calculator.