Factor completely.5, x, squared, minus, 9, x, minus, 25x 2 −9x−2

The expression you provided seems to have a typo. I believe you meant "5x^2 - 9x - 2". Here's how to factor it:

1. First, we need to find two numbers that multiply to (5*-2)=-10 and add to -9. Those numbers are -10 and 1.

2. Rewrite the middle term of the quadratic equation, -9x, as -10x + x.

3. So, the equation becomes 5x^2 - 10x + x - 2.

4. Now, factor by grouping. The first two terms can be grouped together, and the last two terms can be grouped together.

5. Factoring out the greatest common factor from each group gives us: 5x(x - 2) + 1(x - 2).

6. Notice that (x - 2) is a common factor. So, we can factor that out to get: (5x + 1)(x - 2).

So, the factored form of the equation 5x^2 - 9x - 2 is (5x + 1)(x - 2).