To find the solutions of the equation x² – 6x – 22 = 0, we can use the quadratic formula, which is given by:
x = (-b ± √(b² – 4ac)) / 2a
In our equation, a = 1, b = -6, and c = -22. Plugging these values into the quadratic formula:
x = (6 ± √((-6)² – 4(1)(-22))) / (2(1))
Calculating the discriminant:
b² – 4ac = 36 + 88 = 124
Now substituting back into the formula:
x = (6 ± √124) / 2
We can simplify √124:
√124 = √(4 × 31) = 2√31
So now, substituting this back gives:
x = (6 ± 2√31) / 2
Splitting this up:
x = 3 ± √31
Thus, the solutions to the equation x² – 6x – 22 = 0 are:
x = 3 + √31 and x = 3 – √31