One question per post! I will solve No. 9
Solve for x:
x^3 - 4 x^2 + x + 26 = 0
The left hand side factors into a product with two terms:
(x + 2) (x^2 - 6 x + 13) = 0
Split into two equations:
x + 2 = 0 or x^2 - 6 x + 13 = 0
Subtract 2 from both sides:
x = -2 or x^2 - 6 x + 13 = 0
Subtract 13 from both sides:
x = -2 or x^2 - 6 x = -13
Add 9 to both sides:
x = -2 or x^2 - 6 x + 9 = -4
Write the left hand side as a square:
x = -2 or (x - 3)^2 = -4
Take the square root of both sides:
x = -2 or x - 3 = 2 i or x - 3 = -2 i
Add 3 to both sides:
x = -2 or x = 3 + 2 i or x - 3 = -2 i
Add 3 to both sides:
x = -2 or x = 3 + 2 i or x = 3 - 2 i
