Solving the Quadratic Equation x² + 5x – 6 = 0
A quadratic equation is usually in the form of ax² + bx + c = 0, where a, b, and c are constants. In our case, the equation is:
x² + 5x – 6 = 0
Here, we can identify the coefficients as:
- a = 1
- b = 5
- c = -6
1. Using the Quadratic Formula
The quadratic formula is:
x = (-b ± √(b² – 4ac)) / (2a)
Substituting the values of a, b, and c into the formula:
- b² = 5² = 25
- 4ac = 4 × 1 × (-6) = -24
- b² – 4ac = 25 – (-24) = 25 + 24 = 49
Now, we can substitute these values back into the quadratic formula:
x = (-5 ± √49) / (2 × 1)
Since √49 = 7, we have:
x = (-5 ± 7) / 2
2. Finding the Solutions
This gives us two possible solutions:
- x = (-5 + 7) / 2 = 2 / 2 = 1
- x = (-5 – 7) / 2 = -12 / 2 = -6
3. The Solutions
Therefore, the solutions to the quadratic equation x² + 5x – 6 = 0 are:
- x = 1
- x = -6
These solutions indicate that the equation intersects the x-axis at the points (1, 0) and (-6, 0).