To solve the equation x² + 5x = 0 using the quadratic formula, we first need to recognize that this is a quadratic equation of the form ax² + bx + c = 0, where:
- a = 1
- b = 5
- c = 0
The quadratic formula is given by:
x = (-b ± √(b² – 4ac)) / (2a)
Substituting our values into this formula:
x = (–5 ± √(5² – 4 * 1 * 0)) / (2 * 1)
This simplifies to:
x = (–5 ± √(25)) / 2
Since √(25) = 5, we have:
x = (–5 ± 5) / 2
Now, we can calculate the two potential solutions:
- For the positive case:
- For the negative case:
x = (–5 + 5) / 2 = 0 / 2 = 0
x = (–5 – 5) / 2 = –10 / 2 = –5
Thus, the values of x are:
- x = 0
- x = –5