To find a solution for the equation x² – 4x – 10 = 0, we can use the quadratic formula, which is given by:
x = (-b ± √(b² – 4ac)) / 2a
In our case, the coefficients are:
- a = 1
- b = -4
- c = -10
Now, we can calculate the discriminant (b² – 4ac):
Discriminant = (-4)² – 4(1)(-10) = 16 + 40 = 56
Since the discriminant is positive, we have two distinct real solutions. Next, we substitute the values into the quadratic formula:
x = (4 ± √56) / 2
Calculating √56 gives us approximately 7.48. Thus, we have:
x = (4 + 7.48) / 2 ≈ 5.74
and
x = (4 – 7.48) / 2 ≈ -1.74
So the two solutions to the equation x² – 4x – 10 = 0 are approximately x ≈ 5.74 and x ≈ -1.74.