Answer:
x = 5 or x = 5 + 2 i or x = 5 - 2 i
Explanation:
Solve for x:
x^3 - 15 x^2 + 79 x - 145 = 0
Hint: | Factor the left-hand side.
The left hand side factors into a product with two terms:
(x - 5) (x^2 - 10 x + 29) = 0
Hint: | Find the roots of each term in the product separately.
Split into two equations:
x - 5 = 0 or x^2 - 10 x + 29 = 0
Hint: | Look at the first equation: Solve for x.
Add 5 to both sides:
x = 5 or x^2 - 10 x + 29 = 0
Hint: | Look at the second equation: Solve the quadratic equation by completing the square.
Subtract 29 from both sides:
x = 5 or x^2 - 10 x = -29
Hint: | Take one half of the coefficient of x and square it, then add it to both sides.
Add 25 to both sides:
x = 5 or x^2 - 10 x + 25 = -4
Hint: | Factor the left-hand side.
Write the left hand side as a square:
x = 5 or (x - 5)^2 = -4
Hint: | Eliminate the exponent on the left-hand side.
Take the square root of both sides:
x = 5 or x - 5 = 2 i or x - 5 = -2 i
Hint: | Look at the second equation: Solve for x.
Add 5 to both sides:
x = 5 or x = 5 + 2 i or x - 5 = -2 i
Hint: | Look at the third equation: Solve for x.
Add 5 to both sides:
Answer: x = 5 or x = 5 + 2 i or x = 5 - 2 i