\fracn2 (4n + 10) = 150 \implies n(4n + 10) = 300 \implies 4n^2 + 10n - 300 = 0 - Sterling Industries
Solving the Quadratic Equation: \frac{n}{2}(4n + 10) = 150 – Step-by-Step Guide
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.
Image Gallery
Key Insights
Step 1: Eliminate the fraction
To simplify, multiply both sides of the equation by 2:
\[
2 \cdot \frac{n}{2}(4n + 10) = 2 \cdot 150
\]
\[
n(4n + 10) = 300
\]
🔗 Related Articles You Might Like:
📰 "The Ultimate List of the Greatest American Hero Who Changed History Forever 📰 Watch Their Legend Unfold: The Greatest American Hero No One Talks About Enough! 📰 The Girl Downstairs: The Hidden Secret That Explodes Viewer Interest! 📰 Verizon Saline Mi 📰 Import Pdf To Excel 2195316 📰 Jet Ski Racing Game 📰 Oracle Symphony 📰 How To Stop Programs From Running At Startup 📰 Care Portal 📰 Epic Games Parental Control 📰 How To Update Teams 📰 Get Rich Or Die Tryin 📰 Odin Software For Mac 📰 Bank Of America Add Someone To Account 📰 Able Account Fidelity 📰 Verizon 5G Wifi Box 📰 High Saving Rates 📰 How To Check Computer NameFinal 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:
