Expanding the Quadratic Expression: x² − x − 6 = 0 — Solving the Equation Step by Step

Solving quadratic equations is a foundational skill in algebra, essential for students and coding enthusiasts alike. One of the most commonly encountered quadratic expressions is x² − x − 6 = 0. Expanding and solving this equation helps strengthen your understanding of factoring, the quadratic formula, and real-world applications. In this article, we’ll walk through the step-by-step expansion, factoring, and solving of the equation x² − x − 6 = 0, providing clear explanations and practical insight.

Understanding the Context

What is the Quadratic Equation?

A standard quadratic equation takes the form:
ax² + bx + c = 0,
where a, b, and c are constants, and a ≠ 0.

In our example:

  • a = 1
  • b = −1
  • c = −6

Expanding the quadratic allows us to solve for x using factoring, completing the square, or the quadratic formula.

Expandiendo da x^2 - x - 6 = 0.

Key Insights

Step 1: Expanding the Quadratic Expression

Although x² − x − 6 is already expanded, understanding expansion helps when you start with a factored form. Suppose you factor it as:
x² − x − 6 = (x − 3)(x + 2)

Now, expand it using the distributive property:
(x − 3)(x + 2) = x·x + x·2 − 3·x − 3·2 = x² + 2x − 3x − 6 = x² − x − 6

This confirms the factorization is correct.

Continue Reading

You Won’t Believe Which Josh Hutcherson Movies Are Selling Like Hot Cakes!
Josh Hutcherson Movies: The Hidden Gems You’re Threatened to Miss!
From Hits to Flops: Josh Hutcherson’s Movies That Made Headlines (Ranked!)

🔗 Related Articles You Might Like:

📰 Why This Song Makes Kids’ Lullabies Sound Like Ghosts’ Laments 📰 The Most Heartbreaking Funeral Melodies You’ll Never Want to Keep Playing 📰 Your frizzy hair is ruining your day—here’s the secret fix nobody talks about 📰 From Villain To Villainess Discover Why X Men Mystique Dominates Every Story 📰 From Villains To Heroes The Untold Story Behind Yamada Kun And The Seven Witchesshockingly Spicy 📰 From Viral Fame To Xxcharliecxxwatch The Unfiltered Story No Ones Talking About 📰 From Viral Moments To Legend What Made Yoko Taro A Cultural Phenomenon 📰 From Waterfront Charm To Home Staple This Wood Dining Table Is A Must Have 📰 From Waves To Twitter Frenzythis Viral Hashtag Is Unstoppable 📰 From Weak To Wonder Ful The Exact Word That Defines This Person Forever 📰 From Wine To Beer This Surprising Drink Ritual Will Change How You Drink Forever 📰 From Wingstop Ranch To Viral Fame Discover The Hidden Dish Setting Hearts Ablaze 📰 From Wins To Betrayals The Untold Story Of X Men Films You Havent Seen Yet 📰 From Wolverine To Cyclopsx Men Cast Members You Must Watch Again 📰 From Woodstock To Fame The Shocking Origins Of The Character That Changed Music History 📰 From World Title Defenses To Shock Endingshere Are The Top 5 Must Watch Wwe Ppvs 📰 From Wrestlemania Moment To Next Gen Graphics Wwe 2K25 Is Seeing Record Craze 📰 From Wuwa Leaks To Public Frenzyheres What Official Sources Revealed

Final Thoughts

Step 2: Solving x² − x − 6 = 0 by Factoring

Set each factor equal to zero:
(x − 3)(x + 2) = 0

For the product to be zero, either factor must be zero:

  1. x − 3 = 0 → x = 3
  2. x + 2 = 0 → x = −2

solutions: x = 3,         x = −2

Step 3: Using the Quadratic Formula (Alternative Method)

For any ax² + bx + c = 0, the quadratic formula gives:
x = [ −b ± √(b² − 4ac) ] / (2a)

Plugging in a = 1, b = −1, c = −6:
x = [ −(−1) ± √( (−1)² − 4·1·(−6) ) ] / (2·1)
x = [ 1 ± √(1 + 24) ] / 2
x = [ 1 ± √25 ] / 2
x = [ 1 ± 5 ] / 2

Thus:

  • x = (1 + 5)/2 = 6/2 = 3
  • x = (1 − 5)/2 = −4/2 = −2