Question

Solve by inspection. Which two are solutions for x2+3x−28=0 ?(2 points)
Responses

x=−7x is equal to negative 7

x=−4x is equal to negative 4

x=4x is equal to 4

x=7x is equal to 7

Answer 1

To solve the equation \( x^2 + 3x - 28 = 0 \) by inspection, we need to find two numbers that multiply to \(-28\) (the constant term) and add up to \(3\) (the coefficient of \(x\)).

Examining the potential solutions:

1. **\(x = -7\)**: If \(x = -7\):
- The sum: \(-7 + 4 = -3\) (Incorrect)
- The product: \(-7 \cdot 4 = -28\) (Correct)

2. **\(x = -4\)**: If \(x = -4\):
- The sum: \(-4 + 7 = 3\) (Correct)
- The product: \(-4 \cdot 7 = -28\) (Correct)

3. **\(x = 4\)**: If \(x = 4\):
- The sum: \(4 - 7 = -3\) (Incorrect)
- The product: \(4 \cdot -7 = -28\) (Correct)

4. **\(x = 7\)**: If \(x = 7\):
- The sum: \(7 - 4 = 3\) (Correct)
- The product: \(7 \cdot -4 = -28\) (Correct)

The two solutions that fit the equation \(x^2 + 3x - 28 = 0\) are:

**\(x = -4\)** and **\(x = 7\)**.

So the correct answers are:

- \(x = -4\)
- \(x = 7\)