Solving the Quadratic Equation: \frac{n}{2}(4n + 10) = 150 – Step-by-Step Guide

If you've ever encountered an equation like \(\frac{n}{2}(4n + 10) = 150\), you know how powerful algebra can be when solving for unknown variables. This article breaks down how to solve this quadratic equation step by step, showing how to transform, simplify, and apply the quadratic formula to find accurate values of \(n\).

Understanding the Context

Understanding the Equation

We begin with:

\[
\frac{n}{2}(4n + 10) = 150
\]

This equation suggests a proportional relationship multiplied by a linear expression, then set equal to a constant. Solving this will help us uncover the value(s) of \(n\) that satisfy the equation.

Solved: C) (n+1)/n+10 = (n-2)/n+4 [Math]

Image Gallery

Solved: C) (n+1)/n+10 = (n-2)/n+4 [Math]
Solved ∑n=0∞n2+7n+1010 Thes 0/8 ∑n=0∞(1001/(n+2)−1001/(n+3)) | Chegg.com
Solved ∑n=0∞n!n3 ∑n=0∞n2+1n ∑n=0∞10nn! | Chegg.com
Solved 4n+10 6. Let A = [0,1] (-1)" 4n Which of the | Chegg.com
Solved ∑n=130(n2+2)∑n=1020(n3−2n)∑n=010(4i−2i) | Chegg.com

Key Insights

Step 1: Eliminate the fraction

To simplify, multiply both sides of the equation by 2:

\[
2 \cdot \frac{n}{2}(4n + 10) = 2 \cdot 150
\]

\[
n(4n + 10) = 300
\]

Continue Reading

O365 Backup
O365 Business Premium
O365 Business Pricing

🔗 Related Articles You Might Like:

📰 Is Xbox Galaxy the Ultimate Gaming Revolution Youve Been Waiting For? 📰 Xbox Galaxy Explosion: Deep Dive Into the Hottest New Power in Gaming! 📰 You Wont Believe How Xero Stock Skyrocketed in 2024 — Heres Why! 📰 Double Bed Double The Secret To A Dreamy Spacious Night Stay Verified 2055234 📰 Shocked By How Fast Microsoft Mouse Drivers Upgrade Worksdont Miss Out 8256847 📰 How A Michigan First Credit Union Changed My Life Overnightyou Wont Believe It 6232334 📰 Doom Or Opportunity The Surprising Truth About Sprott Inc Stock Today 3150086 📰 Barton Cody 8145782 📰 You Wont Believe What Happens When You Meet The Cenobitethe Mysterious Entity That Haunts Dark Legends 1374347 📰 Ganchada 6530999 📰 This 50 Purple Shirt Is Taking Social Media By Stormheres Why 1652768 📰 The Birdcage Movie 1117716 📰 Wells Fargo Credit Report 7621460 📰 These Monster Trucks Are Shockingplay The Ultimate Team Defining Game Now 2249155 📰 Diagram Of Dfd 657204 📰 Baseball Bats For Sale 215263 📰 Grand Park Royal Cozumel 4561111 📰 Blockbuster Stock Alert Experts Say Its The Next Big Feature Filmheres Why 1196570

Final Thoughts

Now we expand the left-hand side.

Step 2: Expand the quadratic expression

Distribute \(n\) across the parentheses:

\[
n \cdot 4n + n \cdot 10 = 4n^2 + 10n
\]

So the equation becomes:

\[
4n^2 + 10n = 300
\]

Step 3: Bring all terms to one side

To form a standard quadratic equation, subtract 300 from both sides: