Wait — let's solve 3x² + 2 = 425 → x² = 141 → x = √141 → smallest is √141 − 1

How to Solve 3x² + 2 = 425: Step-by-Step Guide & the Smallest Solution (√141 − 1)

Solving quadratic equations is a fundamental math skill that appears in many real-life and academic contexts. Today, we’ll solve the equation 3x² + 2 = 425 step-by-step, explore how to find the exact value of x, and uncover the smallest meaningful solution: √141 − 1. Whether you’re a student, teacher, or math enthusiast, this article will clarify the process and highlight key steps you can apply to similar problems.

Understanding the Context

What Is the Equation?

Start with the given equation:
3x² + 2 = 425

This is a quadratic equation in standard form. To solve for x, we isolate the variable term and simplify.

Image Gallery

Solved Exercise Solve the following problem: min 3x1 – 2x2 - | Chegg.com

Solved: Solve for x. 2x^2+14x+12=0 x=[?], Enter the smallest solution ...

Solved 2. Solve a) 2x - 41-4 = 2 b) |x-1|-250 3. Solve the | Chegg.com

Solved b) Solve 3(x - 2) = 1 + 2(x + 1). same as 3(x-2)/5 = | Chegg.com

Key Insights

Step 1: Isolate the x² Term

Subtract 2 from both sides:
3x² = 425 − 2
3x² = 423

Now divide both sides by 3:
x² = 423 ÷ 3 = 141

So,
x² = 141

🔗 Related Articles You Might Like:

📰 frog's leap winery 📰 brooklyn bridge new york 📰 easton public market 📰 Get Water Out Of Ear 8807787 📰 Discover The Secret Of Hangul That Will Change How You Read Korean Forever 2220940 📰 Buffalo Bills Vs Pittsburgh Steelers Match Player Stats 5024668 📰 5 Ponds Golf 7644842 📰 Service Pack 1 Sp1 For Windows 7 5309 📰 Shoguns 6476535 📰 Average American Salary Revealedis Your Pay Check Catching Up Or Falling Behind 4732118 📰 Windows 10 Free Licence Key 8612055 📰 Norway Prison 7675502 📰 Groupon Is A Scambut Does Everyone Really Know The Real Deal 265736 📰 Visual Script Roblox 4606120 📰 You Wont Believe These Real Cash Withdrawal Games That Pay Real Money Now 7559255 📰 Shocked By These Rare Final Fantasy Trading Card Game Cards Do You Want One Too 9910637 📰 Why This Marine Blue Dress Is Taking Over Coastal Fashion Full Breakdown 6989093 📰 Milada Moore 1605176

Final Thoughts

Step 2: Take the Square Root

To solve for x, take the square root of both sides:
x = ±√141

This gives two solutions: a positive and a negative root — both valid real solutions.

Step 3: Finding the Smallest Solution

The two values are:

x = √141
x = −√141

Since √141 is a positive number (approximately 11.87), the smallest (most negative) real solution is:
√141 − 1 — wait, why?

Actually, √141 − 1 ≈ 10.87, which is not equal to −√141 ≈ −11.87. So there’s a subtle point here.

Let’s clarify: the smallest solution is −√141, not √141 − 1. However, if you’re asked to express the smallest magnitude or a related form, be precise with notation.

But here’s the key insight: while x = −√141 is the smallest real solution, the expression √141 − 1 may appear in related problems — for example, if you subtract 1 from the square root, it reflects a shifted point, not a root.