To solve the equation x² – 30x – 10 = 0, we can use the quadratic formula, which is given by:
x = (-b ± √(b² – 4ac)) / 2a
In our equation, a = 1, b = -30, and c = -10. Let’s substitute these values into the formula:
x = (30 ± √((-30)² – 4 * 1 * (-10))) / (2 * 1)
Now we simplify it step by step:
x = (30 ± √(900 + 40)) / 2
x = (30 ± √940) / 2
√940 can be simplified as:
√940 = √(4 * 235) = 2√235
Now plug that back into our equation:
x = (30 ± 2√235) / 2
Simplifying further:
x = 15 ± √235
Thus, the solution set of the equation x² – 30x – 10 = 0 is:
{ 15 + √235, 15 – √235 }