2x² + 2x – 144 = 0 → x² + x – 72 = 0 - Dyverse
Solving the Quadratic Equation: How to Solve 2x² + 2x – 144 = 0 Using Simplification (x² + x – 72 = 0)
Solving the Quadratic Equation: How to Solve 2x² + 2x – 144 = 0 Using Simplification (x² + x – 72 = 0)
Solve quadratic equations efficiently with a simple algebraic transformation. This article explores how converting the equation 2x² + 2x – 144 = 0 into a simpler form—x² + x – 72 = 0—makes solving for x much easier. Whether you’re a student, educator, or math enthusiast, this step-by-step guide will help you understand the logic and mechanics behind quadratic simplification for faster and clearer results.
Understanding the Context
Introduction to Quadratic Equations
Quadratic equations are polynomial equations of the second degree, typically expressed in the standard form:
ax² + bx + c = 0
Common examples include ax² + bx + c = 0, where a ≠ 0. These equations can yield two real solutions, one real solution, or complex roots, depending on the discriminant b² – 4ac. One key strategy to solving quadratics is completing the transformation to standard form—often by simplifying coefficients.
Key Insights
In this post, we focus on the effective trick of dividing the entire equation by 2 to reduce complexity: turning 2x² + 2x – 144 = 0 into x² + x – 72 = 0.
Step-by-Step Conversion: From 2x² + 2x – 144 = 0 to x² + x – 72 = 0
Original Equation:
2x² + 2x – 144 = 0
Divide all terms by 2 (to simplify coefficients):
(2x²)/2 + (2x)/2 – 144/2 = 0
🔗 Related Articles You Might Like:
📰 This Shyamalan Classic Hooks You with Shocking Secrets You Missed the First Time! 📰 From Twists to Hidden Truths—Here’s Why M Night Shyamalan Still Scaresthe Screen! 📰 Nobody Saw These Shyamalan Twists Coming—Explore His Most Mind-Blowing Movies Now! 📰 The Devastating Lethal Path Of Trap Shooting Before Its Too Late 📰 The Devastating Reason Vermonts One Point Margin Victory Will Go Down In History 📰 The Devastating Secret Behind Who Really Controls Texass Future 📰 The Diaper Pail That Changed Everythingyou Wont Believe Whats Inside 📰 The Divine Language Of Vishnu Sahastra Unlockedsecrets That Unlock Cosmic Power 📰 The Dolls Wont Sleepthey Demand You Juggle Them Or Lose Everything 📰 The Dolly Hidden In The Shadows No One Saw It Coming 📰 The Dolly That Changed Every Shot Forever Watch Now 📰 The Dramatic Differences Between Hair Types No One Notices 📰 The Dramatic Way This Workshop Transformed My Vocabulary Overnight 📰 The Dress That Defied Tradition Vivienne Westwoods Unveiled Wedding Masterpiece 📰 The Early Signs Of Warping Or Swelling Are Cracking The Truth Of Whats Really Happening 📰 The Earrings That Sparked Firecustomest Vivienne Westwood Piece Revealed In Secret 📰 The East Boston Man Shocks Fans In His Nondocumentary Look 📰 The Egg Came Firstdiscover The Ancient Secret No One Talks AboutFinal Thoughts
Simplifies to:
x² + x – 72 = 0
Now the equation is simpler yet retains its core quadratic structure and key constants. The discriminant remains unchanged and easy to compute.
Why Simplify: The Benefits of Reformulating the Equation
Simplifying quadratic equations offers clear advantages:
- Fewer coefficients to track: Smaller numbers reduce arithmetic errors.
- Faster solution processing: Approaches like factoring, completing the square, or the quadratic formula become quicker.
- Clearer insight: Recognizing patterns—such as factorable pairs—becomes more manageable.
In our case, dividing by 2 reveals that the equation relates directly to integers:
x² + x = 72 → (x² + x – 72 = 0)
This form perfectly sets up methods like factoring, quadratic formula, or estimation.
