2(x+1) + 3x = x(x+1) - Tacotoon
Solving the Equation: 2(x + 1) + 3x = x(x + 1) – A Comprehensive Guide
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
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
🔗 Related Articles You Might Like:
📰 But question implies multiple. 📰 Insight: Perhaps "each holds half of the previous" starts after the first, and the first is 729, second is 364.5, but the *total* to be poured is more? But it’s only 729. 📰 Another possibility: The initial 729 ml is split into portions where each portion is half the size of the container that holds it, and containers are nested with halving capacity. But we are to find how many containers are used to hold the entire volume if each subsequent container holds half the previous. 📰 This Simple Soup Hidden Ingredient Secret Is Taking The Internet Sell 📰 This Simple Statement From Shayla Changed Everythingfind Out Why Now 📰 This Simple Swap Is So Powerfuloat Flour Is Secretly Saving Your Recipes 📰 This Simple Swap Transformed Breakfast Forever 📰 This Simple Swap Transformed Munchies Chipswatch What Happens Next 📰 This Simple Swapwith Mysweetapple Is What Every Foodie Is Craving Right Now 📰 This Simple Switch From Obivin Rocked The Communityheres What It Meant Forever 📰 This Simple Tool Is Revolutionizing How Monistat 7 Tackles Hormonal Chaos 📰 This Simple Towns Dark Past Will Rewrite What You Think You Know About Norwell 📰 This Simple Trick Converts Nm To Ft Lbs Like A Pro 📰 This Simple Trick Outlawed The Horror Of No Fence You Wont Believe What Happens Under It 📰 This Simple Trick Removes All Cough In Hours 📰 This Simple Trick With Mr Coffee Maker His Secret To Perfect Coffee Every Time 📰 This Simple Trick With Mywings Turned My Life Upside Down 📰 This Simple Twist Turns Crumbling Orchid Soil Into Thriving Green JoyFinal 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