Answer:
x = 0 or x = sqrt(21)/2 - 1/2 or x = -1/2 - sqrt(21)/2
Step-by-step explanation:
Solve for x over the real numbers:
(3 x^3 + 4 x^2) - (2 x^3 + 3 x^2 - x) = (3 3 x + 4 2 x) - (2 3 x + 3 2 x - x)
(3 x^3 + 4 x^2) - (2 x^3 + 3 x^2 - x) = x^3 + x^2 + x and (3 x 3 + 4 x 2) - (2 x 3 + 3 x 2 - x) = 6 x:
x^3 + x^2 + x = 6 x
Subtract 6 x from both sides:
x^3 + x^2 - 5 x = 0
Factor x from the left hand side:
x (x^2 + x - 5) = 0
Split into two equations:
x = 0 or x^2 + x - 5 = 0
Add 5 to both sides:
x = 0 or x^2 + x = 5
Add 1/4 to both sides:
x = 0 or x^2 + x + 1/4 = 21/4
Write the left hand side as a square:
x = 0 or (x + 1/2)^2 = 21/4
Take the square root of both sides:
x = 0 or x + 1/2 = sqrt(21)/2 or x + 1/2 = -sqrt(21)/2
Subtract 1/2 from both sides:
x = 0 or x = sqrt(21)/2 - 1/2 or x + 1/2 = -sqrt(21)/2
Subtract 1/2 from both sides:
Answer: x = 0 or x = sqrt(21)/2 - 1/2 or x = -1/2 - sqrt(21)/2
