Question

Solve 2x2+8x=0
2
𝑥
2
+
8
𝑥
=
0
by factoring out the greatest common factor.

Enter your solutions as an integer.

(2 points)
x =
𝑥

=


x=
𝑥
=

Answer 1

To solve the equation \( 2x^2 + 8x = 0 \) by factoring out the greatest common factor, we can follow these steps:

1. **Factor out the greatest common factor (GCF)**:
The GCF of \( 2x^2 \) and \( 8x \) is \( 2x \).
So we factor the equation:

\[
2x(x + 4) = 0
\]

2. **Set each factor equal to zero**:
Now we set each factor to zero:
\[
2x = 0
\]
\[
x + 4 = 0
\]

3. **Solve each equation**:
- From \( 2x = 0 \):
\[
x = 0
\]

- From \( x + 4 = 0 \):
\[
x = -4
\]

4. **Write the solutions**:
So the solutions are:
\[
x = 0 \quad \text{and} \quad x = -4
\]

Thus, the final answers are:
\[
x = 0
\]
\[
x = -4
\]