Question

Solve the equation 0=3x2−4x+1
by factoring. One of the solutions is provided. What is the other solution?(1 point)
The solutions are x=13
and x=

Answer 1

To solve the equation \( 0 = 3x^2 - 4x + 1 \) by factoring, we can start by factoring the quadratic expression.

1. We can rewrite the equation:
\[
3x^2 - 4x + 1 = 0
\]

2. We need to find two numbers that multiply to \( 3 \times 1 = 3 \) (the product of \( a \) and \( c \)) and add up to \( -4 \) (the coefficient of \( x \)). The two numbers that satisfy these conditions are \( -3 \) and \( -1 \).

3. We can rewrite the middle term using these numbers:
\[
3x^2 - 3x - x + 1 = 0
\]

4. Next, we group the terms:
\[
(3x^2 - 3x) + (-x + 1) = 0
\]

5. Factor out the common factors from each group:
\[
3x(x - 1) - 1(x - 1) = 0
\]

6. Now, factor out the common factor \( (x - 1) \):
\[
(3x - 1)(x - 1) = 0
\]

7. Now we can set each factor equal to zero:
\[
3x - 1 = 0 \quad \text{or} \quad x - 1 = 0
\]

- Solving \( 3x - 1 = 0 \):
\[
3x = 1 \implies x = \frac{1}{3}
\]

- Solving \( x - 1 = 0 \):
\[
x = 1
\]

So, the two solutions are:
\[
x = \frac{1}{3} \quad \text{and} \quad x = 1
\]

Since the problem states that one of the solutions is \( x = \frac{1}{3} \), the other solution is:
\[
\boxed{1}
\]