Answer:
x = -2 or x = -6 or x = sqrt(5) or x = -sqrt(5)
Step-by-step explanation:
Solve for x:
x^4 + 8 x^3 + 7 x^2 - 40 x - 60 = 0
The left hand side factors into a product with three terms:
(x + 2) (x + 6) (x^2 - 5) = 0
Split into three equations:
x + 2 = 0 or x + 6 = 0 or x^2 - 5 = 0
Subtract 2 from both sides:
x = -2 or x + 6 = 0 or x^2 - 5 = 0
Subtract 6 from both sides:
x = -2 or x = -6 or x^2 - 5 = 0
Add 5 to both sides:
x = -2 or x = -6 or x^2 = 5
Take the square root of both sides:
Answer: x = -2 or x = -6 or x = sqrt(5) or x = -sqrt(5)
