Question

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

Enter your solutions as an integer.

(2 points)
x =


x=

Answer 1

To solve the equation \(2x^2 + 8x = 0\) by factoring out the greatest common factor, let's start by identifying it.

1. The greatest common factor of \(2x^2\) and \(8x\) is \(2x\).
2. We can factor the equation:

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

3. Now, we can set each factor equal to zero:

\[
2x = 0 \quad \text{or} \quad x + 4 = 0
\]

4. Solving these equations gives:

For \(2x = 0\):
\[
x = 0
\]

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

Thus, the solutions are:

\[
x = 0
\]
\[
x = -4
\]

So the final answers are:

\(x = 0\)

\(x = -4\)