What are the solutions to the quadratic equation x² + 5x?

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To solve the quadratic equation x² + 5x = 0, we can utilize the method of factoring. First, let’s factor the equation to find its roots.

1. Begin by rewriting the equation:

x² + 5x = 0

2. Next, factor out the common term, which is x:

x(x + 5) = 0

3. Now, set each factor equal to zero:

  • x = 0
  • x + 5 = 0
    This simplifies to x = -5

So, the two solutions to the quadratic equation x² + 5x = 0 are:

  • x = 0
  • x = -5

These solutions indicate the points at which the parabola described by the equation intersects the x-axis. You can visualize this quadratic function, which opens upwards, to see how these values correspond to the roots on a graph.

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