Solving the Equation: 2(x + 1) + 3x = x(x + 1) – A Comprehensive Guide

When faced with algebraic equations, simplifying both sides and solving for the variable can sometimes seem challenging. One common equation that students and math enthusiasts often explore is:
2(x + 1) + 3x = x(x + 1)

This equation represents a powerful exercise in algebraic manipulation and problem-solving. In this SEO-optimized article, we break down the full process of solving 2(x + 1) + 3x = x(x + 1), providing clear steps, real-world applications, and useful keywords to help improve search visibility for educators and learners alike.

Understanding the Context

Understanding the Equation

The equation
2(x + 1) + 3x = x(x + 1)
contains both linear and quadratic components. The left side involves distribution and combination of like terms, while the right side expands into a polynomial. Solving this equation helps reinforce skills in:

  • Distributing parentheses
  • Combining like terms
  • Expanding binomials
  • Solving first-degree and quadratic equations
Solved 2x-1 (x+1) | Chegg.com

Image Gallery

Solved 2x-1 (x+1) | Chegg.com
SOLVED:2(x+3)=3(x-1)
Solved: 2) (x+1)/3x-4 - (2x-3)/4+3x [Math]
Solved: |2 x+1|
Solved: the tonowimg expressions 3x(x+1)(x-1) and 2x^2(x-1)(x+3) [algebra]

Key Insights

Step-by-Step Solution

Step 1: Expand Both Sides

Start by expanding each term using algebraic properties.

Left-hand side (LHS):
2(x + 1) + 3x
= 2·x + 2·1 + 3x
= 2x + 2 + 3x
= (2x + 3x) + 2
= 5x + 2

Continue Reading

water flter
water brand water
greater libertyville soccer association

🔗 Related Articles You Might Like:

📰 Unlock the Secret to Scoring Top Marks with This Free AP Chem Equation Sheet! 📰 The Ultimate AP Chem Equation Sheet That Will Change How You Study Forever! 📰 Shocked Your AP Chem Exam? Fix It with This Essential Equation Sheet! 📰 Toxicology 501332 📰 Umb Financial Corporation Exposed Shocking Secrets Behind Its Shoes On Business Empire 9580108 📰 Wells Fargo Banking Down 5532265 📰 Knight Office Solutions 2050897 📰 Wheelie Games 8147946 📰 Why Everyones Talking About The Department Of Health Federalbreakdown Of Major Implications 2350580 📰 Can Walnuts Kill Your Dog The Scariest Truth About This Simple Nut 8896248 📰 Master Every Detailing Step In The Hottest Petrol Station Simulator Game Now 6508834 📰 This Simple Cupcake Box Transforms Your Treats Into Instagram Worthy Wonders 9485234 📰 5 Shocking Voice Memo Found On Iphoneyoull Never Forget This 9344993 📰 End Of Day Shocker Stock Exchange Closes At What Exact Time Get The Full Timeline Now 1101241 📰 Best Us Exchange Rate 355368 📰 1V1Lol Game 7281561 📰 Quasi War 4929337 📰 Youll Never Guess Whats Causing Your Laptop Display To Flashfix It Now 5169419

Final Thoughts

Right-hand side (RHS):
x(x + 1)
= x·x + x·1
= x² + x

So the equation becomes:
5x + 2 = x² + x

Step 2: Move All Terms to One Side

To solve for x, bring all terms to one side to form a standard quadratic equation:
x² + x – 5x – 2 = 0
→ x² – 4x – 2 = 0

Step 3: Solve the Quadratic Equation

Use the quadratic formula:
x = [−b ± √(b² – 4ac)] / (2a)
For x² – 4x – 2 = 0,
a = 1, b = –4, c = –2

Calculate the discriminant:
Δ = b² – 4ac = (−4)² – 4(1)(–2) = 16 + 8 = 24

Roots:
x = [4 ± √24] / 2
√24 = √(4×6) = 2√6, so
x = [4 ± 2√6] / 2
→ x = 2 ± √6