To solve the factored quadratic equation \( (13x - 2)(x - 34) = 0 \), we can use the zero product property, which states that if the product of two factors is equal to zero, then at least one of the factors must be equal to zero.
We set each factor to zero:
- \( 13x - 2 = 0 \)
- \( x - 34 = 0 \)
Now, let's solve each equation separately.
For the first factor:
\[ 13x - 2 = 0 \]
Add 2 to both sides:
\[ 13x = 2 \]
Now, divide by 13:
\[ x = \frac{2}{13} \]
For the second factor:
\[ x - 34 = 0 \]
Add 34 to both sides:
\[ x = 34 \]
So, the solutions to the equation \( (13x - 2)(x - 34) = 0 \) are:
\[ x = \frac{2}{13} \quad \text{and} \quad x = 34 \]
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