Question

The product of two consecutive even integers is 2208. What is their sum?

Answer 1

±94

General Formulas and Concepts:

Pre-Algebra

• Order of Operations: BPEMDAS
• Equality Properties

Algebra I

• Standard Form: ax² + bx + c = 0
• Solving Quadratic Equations
• Consecutive Integers

Explanation:

Step 1: Define

x (1st consecutive term)

x + 2 (2nd consecutive term)

Step 2: Set up equation

x(x + 2) = 2208

Step 3: Solve for x

1. Distribute x: x² + 2x = 2208
2. Rewrite in Standard Form: x² + 2x - 2208 = 0
3. Factor quadratic: (x - 46)(x + 48) = 0
4. Find roots: x = -48, 46

Step 4: Identify Consecutive Integers

Possibility 1: x = -48

1st Consecutive Even Term: -48

2nd Consecutive Even Term: -48 + 2 = -46

Possibility 2: x = 46

1st Consecutive Even Term: 46

2nd Consecutive Even Term: 46 + 2 = 48

Step 5: Find sums

Possibility 1: x = -48

-48 + -46 = -94

Possibility 2: x = 46

46 + 48 = 94