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'll first try to factor the quadratic expression.

The given equation can be rearranged as:

\[
3x^2 - 4x + 1 = 0
\]

To factor this, we need two numbers that multiply to \( 3 \times 1 = 3 \) (the product of the leading coefficient and the constant term) and add to \(-4\) (the coefficient of the linear term).

The numbers that meet these criteria are \(-3\) and \(-1\). Therefore, we can rewrite \(-4x\) as \(-3x - x\):

\[
3x^2 - 3x - x + 1 = 0
\]

Now, we can group the terms:

\[
(3x^2 - 3x) + (-x + 1) = 0
\]

Factoring out common factors from each group gives:

\[
3x(x - 1) - 1(x - 1) = 0
\]

Now we can factor by grouping:

\[
(3x - 1)(x - 1) = 0
\]

Setting each factor equal to zero gives us the solutions:

1. \( 3x - 1 = 0 \) ⇒ \( 3x = 1 \) ⇒ \( x = \frac{1}{3} \)
2. \( x - 1 = 0 \) ⇒ \( x = 1 \)

You provided one of the solutions as \( x = \frac{1}{3} \). Therefore, the other solution is:

\[
x = 1
\]

Thus, the other solution is \( x = 1 \).