9514 1404 393
Answer:
x = -2 and x = 1/3
Step-by-step explanation:
The simple way to solve this is to enter the equation into a graphing calculator and have it show you what the zeros are.
The solutions are x = -2 and x = 1/3.
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One way to solve this is to factor it. The product of the leading coefficient and the constant is (3)(-2) = -6. You want to find factors of this number that have a sum equal to the coefficient of the linear term: 5.
-6 = (-1)(6) = (-2)(3) = ...
The first pair of factors listed here has a sum of 5, so we can rewrite the equation as ...
3x^2 -x +6x -2 = 0
Factoring pairs of terms, we have ...
x(3x -1) +2(3x -1) = 0
(x +2)(3x -1) = 0
The solutions are the values of x that make these factors zero:
x + 2 = 0 ⇒ x = -2
3x -1 = 0 ⇒ x = 1/3
The solutions are x = -2 and x = 1/3.
