Answer:
x = -1/5
Step-by-step explanation:
Solve for x over the real numbers:
10 x^3 - 13 x^2 + 12 x + 3 = 0
The left hand side factors into a product with two terms:
(5 x + 1) (2 x^2 - 3 x + 3) = 0
Split into two equations:
5 x + 1 = 0 or 2 x^2 - 3 x + 3 = 0
Subtract 1 from both sides:
5 x = -1 or 2 x^2 - 3 x + 3 = 0
Divide both sides by 5:
x = -1/5 or 2 x^2 - 3 x + 3 = 0
Divide both sides by 2:
x = -1/5 or x^2 - (3 x)/2 + 3/2 = 0
Subtract 3/2 from both sides:
x = -1/5 or x^2 - (3 x)/2 = -3/2
Add 9/16 to both sides:
x = -1/5 or x^2 - (3 x)/2 + 9/16 = -15/16
Write the left hand side as a square:
x = -1/5 or (x - 3/4)^2 = -15/16
(x - 3/4)^2 = -15/16 has no solution since for all x on the real line, (x - 3/4)^2 >=0 and -15/16<0:
Answer: x = -1/5
