Question

Solve each quadratic equation. Write your answer as a simplified fraction when applicable. Write the lesser number first.

(1 point)
Quadratic Equation Your Answer
1 (x+3)(x−1)=0
x =
and x =
2 (15x−5)(7+x)=0
x =
and x =
3 (13x−2)(x−34)=0
x =
and x =
4 30=x2+13x
x =
and x =

Answer 1

Let's solve each quadratic equation step by step.

### Problem 1: \( (x + 3)(x - 1) = 0 \)

To solve this equation, we set each factor to zero:

1. \( x + 3 = 0 \) → \( x = -3 \)
2. \( x - 1 = 0 \) → \( x = 1 \)

Thus, the answers are:
- \( x = -3 \)
- \( x = 1 \)

### Problem 2: \( (15x - 5)(7 + x) = 0 \)

Set each factor to zero:

1. \( 15x - 5 = 0 \)
- \( 15x = 5 \)
- \( x = \frac{5}{15} = \frac{1}{3} \)

2. \( 7 + x = 0 \)
- \( x = -7 \)

Thus, the answers are:
- \( x = -7 \)
- \( x = \frac{1}{3} \)

### Problem 3: \( (13x - 2)(x - 34) = 0 \)

Set each factor to zero:

1. \( 13x - 2 = 0 \)
- \( 13x = 2 \)
- \( x = \frac{2}{13} \)

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

Thus, the answers are:
- \( x = \frac{2}{13} \)
- \( x = 34 \)

### Problem 4: \( 30 = x^2 + 13x \)

Rearrange to standard form:

\[
x^2 + 13x - 30 = 0
\]

Now we can factor or use the quadratic formula. Let's factor this:

We need two numbers that multiply to \(-30\) and add up to \(13\):
- The numbers are \(15\) and \(-2\).

So we can factor the equation:

\[
(x + 15)(x - 2) = 0
\]

Set each factor to zero:

1. \( x + 15 = 0 \)
- \( x = -15 \)

2. \( x - 2 = 0 \)
- \( x = 2 \)

Thus, the answers are:
- \( x = -15 \)
- \( x = 2 \)

### Summary of Solutions:

1. \( (x + 3)(x - 1) = 0 \)
\( x = -3 \) and \( x = 1 \)

2. \( (15x - 5)(7 + x) = 0 \)
\( x = -7 \) and \( x = \frac{1}{3} \)

3. \( (13x - 2)(x - 34) = 0 \)
\( x = \frac{2}{13} \) and \( x = 34 \)

4. \( 30 = x^2 + 13x \)
\( x = -15 \) and \( x = 2 \)