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mrs_skeptik [129]
2 years ago
7

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

Mathematics
1 answer:
Katena32 [7]2 years ago
6 0

Answer:

±94

General Formulas and Concepts:

<u>Pre-Algebra</u>

  • Order of Operations: BPEMDAS
  • Equality Properties

<u>Algebra I</u>

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

Step-by-step explanation:

<u>Step 1: Define</u>

<em>x</em>  (1st consecutive term)

<em>x + 2</em> (2nd consecutive term)

<u>Step 2: Set up equation</u>

x(x + 2) = 2208

<u>Step 3: Solve for </u><em><u>x</u></em>

  1. Distribute <em>x</em>:                                   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

<u>Step 4: Identify Consecutive Integers</u>

<em>Possibility 1: x = -48</em>

1st Consecutive Even Term: -48

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

<em />

<em>Possibility 2: x = 46</em>

1st Consecutive Even Term: 46

2nd Consecutive Even Term: 46 + 2 = 48

<u>Step 5: Find sums</u>

<em>Possibility 1: x = -48</em>

-48 + -46 = -94

<em>Possibility 2: x = 46</em>

46 + 48 = 94

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