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.

Question

We set each factor to zero:

1. \( 13x - 2 = 0 \)
2. \( x - 34 = 0 \)

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:**

\[
x = \frac{2}{13} \quad \text{and} \quad x = 34
\]
make this like a 6th grader wrote it

Answer 1

To solve the equation \( (13x - 2)(x - 34) = 0 \), we can use something called the zero product property. This means if you multiply two things together and get zero, then at least one of those things must be zero.

So, we set each part (or "factor") equal to zero:

1. \( 13x - 2 = 0 \)
2. \( x - 34 = 0 \)

Now, let’s solve each one!

For the first part:

\[ 13x - 2 = 0 \]

To get rid of the -2, we add 2 to both sides:

\[ 13x = 2 \]

Next, we need to get \( x \) by itself. Since \( x \) is being multiplied by 13, we divide by 13:

\[ x = \frac{2}{13} \]

For the second part:

\[ x - 34 = 0 \]

Here, we just add 34 to both sides to solve for \( x \):

\[ x = 34 \]

So, the answers to the equation \( (13x - 2)(x - 34) = 0 \) are:

\[ x = \frac{2}{13} \quad \text{and} \quad x = 34 \]

That’s it! We found both solutions!