To solve the quadratic equation x² – 8x – 12 = 0, we can use the quadratic formula, which is given by:
x = (-b ± √(b² – 4ac)) / (2a)
In this equation, a = 1, b = -8, and c = -12. Plugging these values into the formula, we first calculate the discriminant (b² – 4ac):
Step 1: Calculate the discriminant
b² – 4ac = (-8)² – 4(1)(-12) = 64 + 48 = 112
Step 2: Use the quadratic formula
Now we substitute the values into the formula:
x = (8 ± √112) / (2 * 1)
To simplify √112, we can break it down:
√112 = √(16 × 7) = 4√7
So, substituting back, we have:
x = (8 ± 4√7) / 2
Dividing each term by 2 gives us:
x = 4 ± 2√7
Conclusion:
The solution set of the equation x² – 8x – 12 = 0 is:
x = 4 + 2√7 and x = 4 – 2√7.