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:

📰 Revamp Your Bathroom Decor with These Must-Have Bathroom Signs! 📰 Boost Your Bathroom’s Style & Safety: Top Bath Signs You Can’t Ignore! 📰 This Bath Tray Will Transform Your Bathroom into a Luxury Oasis – Don’t Miss These Hidden Features! 📰 H The Exploration Of Subjective Experience In Biological Contexts 3814292 📰 Rusm Domnica Is Hereyour Dream Tropical Escape Awaits Everyone 2341296 📰 U Miami 5271432 📰 Struggling With Excel The Top 5 Vba Applications That Every User Should Master Asap 6471184 📰 How Long Is A Centimetre 6930302 📰 Where Sudan Located 938878 📰 Find Any Stone Like Never Before The Ultimate Stone Identifier Revealed 915620 📰 Upended 7788935 📰 Why This Screen Mirroring App Is The Best For Your Macbook Air Proof Inside 8164338 📰 Gameboy Gba Roms 8569239 📰 You Wont Believe How Expensive It Really Is To Install Premium Hardwood 6174149 📰 Eastern Exorcist 2628649 📰 Discover Orion Dc The Mysterious Universe Thats Changing Urban Gaming Forever 751193 📰 World Rhyming 9644385 📰 A Silent Voice Manga 6367017

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.