Question

Solve by inspection. Which two are solutions for x2−x−6=0
?

Select two solutions.

(2 points)
Responses

x=−2
x is equal to negative 2

x=−3
x is equal to negative 3

x=3
x is equal to 3

x=2

Answer 1

To solve the equation \(x^2 - x - 6 = 0\) by inspection, we can factor the left side.

We can rewrite \(x^2 - x - 6\) as follows:

\[
x^2 - 3x + 2x - 6 = 0
\]

Now, we group the terms:

\[
(x^2 - 3x) + (2x - 6) = 0
\]

Factoring out the common factors, we get:

\[
x(x - 3) + 2(x - 3) = 0
\]

This can be factored as:

\[
(x - 3)(x + 2) = 0
\]

Setting each factor to zero gives us the solutions:

1. \(x - 3 = 0 \Rightarrow x = 3\)
2. \(x + 2 = 0 \Rightarrow x = -2\)

Thus, the two solutions for the equation \(x^2 - x - 6 = 0\) are:

- \(x = -2\)
- \(x = 3\)

So, the correct selections are:

- x = -2
- x = 3