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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=
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1 answer

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