Final answer:
To solve the quadratic equation x² + 14x + 17 = -96, rearrange it to x² + 14x + 113 = 0 and use the quadratic formula to find the solutions.
Step-by-step explanation:
To solve the quadratic equation x² + 14x + 17 = -96, we need to rearrange it so that it equals 0:
x² + 14x + 113 = 0
Now we can use the quadratic formula to find the two possible values of x:
x = (-b ± sqrt(b² - 4ac)) / 2a
- a = 1, b = 14, c = 113
- x = (-14 ± sqrt(14² - 4(1)(113))) / 2(1)
- x = (-14 ± sqrt(196 - 452)) / 2
- x = (-14 ± sqrt(-256)) / 2
- Since the discriminant is negative, the quadratic equation has no real solutions.