To solve the equation x² – 6x – 40 = 0, we can use the quadratic formula, which is given by:
x = (-b ± √(b² – 4ac)) / (2a)
In this case, the coefficients are:
- a = 1
- b = -6
- c = -40
First, we need to calculate the discriminant, which is b² – 4ac:
b² – 4ac = (-6)² – 4(1)(-40) = 36 + 160 = 196
Since the discriminant is positive, it indicates that there are two distinct real solutions. Now we can substitute the values into the quadratic formula:
x = (6 ± √196) / (2 * 1)
Calculating the square root of 196:
√196 = 14
Now we substitute this back into the formula:
x = (6 ± 14) / 2
This gives us two possible solutions:
- x₁ = (6 + 14) / 2 = 20 / 2 = 10
- x₂ = (6 – 14) / 2 = -8 / 2 = -4
Thus, the solutions to the equation x² – 6x – 40 = 0 are:
x = 10 and x = -4.