Answer:
x = 4 or x = -2
Step-by-step explanation:
Solve for x over the real numbers:
x^4 - 9 x^2 - 22 x - 24 = 0
The left hand side factors into a product with three terms:
(x - 4) (x + 2) (x^2 + 2 x + 3) = 0
Split into three equations:
x - 4 = 0 or x + 2 = 0 or x^2 + 2 x + 3 = 0
Add 4 to both sides:
x = 4 or x + 2 = 0 or x^2 + 2 x + 3 = 0
Subtract 2 from both sides:
x = 4 or x = -2 or x^2 + 2 x + 3 = 0
Subtract 3 from both sides:
x = 4 or x = -2 or x^2 + 2 x = -3
Add 1 to both sides:
x = 4 or x = -2 or x^2 + 2 x + 1 = -2
Write the left hand side as a square:
x = 4 or x = -2 or (x + 1)^2 = -2
(x + 1)^2 = -2 has no solution since for all x on the real line, (x + 1)^2 >=0 and -2<0:
Answer: x = 4 or x = -2
