Question

0 = x^2 - 6x - 20

1.?
2.?
3?

Answer 1

To solve the equation \(0 = x^2 - 6x - 20\), we can either factor it, complete the square, or use the quadratic formula. Here, we will factor it.

1. **Factoring the equation**:
We need to find two numbers that multiply to \(-20\) (the constant term) and add to \(-6\) (the coefficient of \(x\)). These numbers are \(-10\) and \(+4\).

So, we can factor the quadratic as:
\[
0 = (x - 10)(x + 4)
\]

2. **Setting each factor to zero**:
We set each factor equal to zero to find the solutions for \(x\).
\[
x - 10 = 0 \quad \text{or} \quad x + 4 = 0
\]

3. **Solving for \(x\)**:
- From \(x - 10 = 0\), we get:
\[
x = 10
\]
- From \(x + 4 = 0\), we get:
\[
x = -4
\]

Thus, the solutions to the equation \(0 = x^2 - 6x - 20\) are:
1. \(x = 10\)
2. \(x = -4\)

If you are looking for a specific format for the numbered list, please clarify what you need for points 1, 2, and 3, and I can adjust accordingly!