To solve the quadratic equation x² + 5x = 0 using the quadratic formula, we first need to identify the coefficients in the standard form of a quadratic equation, which is ax² + bx + c = 0.
In our equation, we have:
- a = 1
- b = 5
- c = 0
The quadratic formula is:
x = (-b ± √(b² – 4ac)) / (2a)
We can now substitute the values of a, b, and c into the formula:
x = (-5 ± √(5² - 4 * 1 * 0)) / (2 * 1)
Calculating the discriminant:
5² - 4 * 1 * 0 = 25 - 0 = 25
Now we substitute this back into the formula:
x = (-5 ± √25) / 2
Since √25 = 5, we have:
x = (-5 ± 5) / 2
This gives us two potential solutions:
x = (-5 + 5) / 2 = 0 / 2 = 0
x = (-5 - 5) / 2 = -10 / 2 = -5
Therefore, the values of x that satisfy the equation x² + 5x = 0 are:
- x = 0
- x = -5