Steps in Solving Quadratic Equations by Extracting Roots:

To solve a quadratic equation by extracting roots, we need to follow a few steps. This method is particularly useful when the quadratic equation can be factorized into two linear factors. Here are the detailed steps:

1. Identify the Quadratic Equation:
- A quadratic equation is a polynomial equation of degree 2, represented in the form: ax^2 + bx + c = 0, where a, b, and c are constants and 'a' is not equal to 0.
- For example, let's consider the quadratic equation: x^2 - 5x + 6 = 0.

2. Factorize the Quadratic Equation:
- In this step, we factorize the quadratic equation into two linear factors.
- For the example equation x^2 - 5x + 6 = 0, we can factorize it as (x - 2)(x - 3) = 0.

3. Set Each Factor Equal to Zero:
- By setting each factor equal to zero, we can find the values of 'x' that satisfy the equation.
- Setting (x - 2) = 0 gives x = 2.
- Setting (x - 3) = 0 gives x = 3.

4. Write Down the Solutions:
- The solutions of the quadratic equation are the values of 'x' that satisfy the equation.
- In this case, the solutions are x = 2 and x = 3.

5. Verify the Solutions:
- After obtaining the solutions, it is important to verify if they satisfy the original quadratic equation.
- Substituting x = 2 and x = 3 into the equation x^2 - 5x + 6 = 0, we get (2)^2 - 5(2) + 6 = 0 and (3)^2 - 5(3) + 6 = 0, which are true.
- Therefore, the solutions x = 2 and x = 3 are valid solutions to the given quadratic equation.

By following these steps, we can solve quadratic equations by extracting roots. It is important to remember that not all quadratic equations can be easily factorized, and in such cases, other methods like the quadratic formula may be employed to find the solutions.