To solve the equation x² + 5x = 0 using the quadratic formula, we start by recognizing that this is a quadratic equation in the standard form ax² + bx + c = 0.
In this case, we can identify the coefficients as follows:
- a = 1 (the coefficient of x²)
- b = 5 (the coefficient of x)
- c = 0 (the constant term)
The quadratic formula is:
x = (-b ± √(b² – 4ac)) / (2a)
Plugging our values into the formula:
x = ( -5 ± √(5² – 4 * 1 * 0) ) / (2 * 1)
Calculating the discriminant:
- 5² = 25
- 4 * 1 * 0 = 0
- 25 – 0 = 25
Now substituting back into the formula:
x = (-5 ± √25) / 2
Calculating the square root:
- √25 = 5
So we have:
x = (-5 ± 5) / 2
This results in two possible solutions for x:
- 1st solution: x = (-5 + 5) / 2 = 0 / 2 = 0
- 2nd solution: x = (-5 – 5) / 2 = -10 / 2 = -5
Thus, the values of x that satisfy the equation x² + 5x = 0 are:
- x = 0
- x = -5
To summarize, the solutions are:
x = 0 and x = -5.