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.

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

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:

📰 jaquar 📰 jar jar binks actor 📰 jar jar binks sith lord 📰 This Oven Transforms Chicken Into Craving Perfectionepic Results 📰 This Overall Dress Is Hiding A Secret That No One Expected 📰 This Overall Dress Is Not Just Clothesits A Game Changer Worth Every Penny 📰 This Overlooked Ingredient Holds The Key To Garlic Beyond The Ordinarywatch Now 📰 This Overlooked Peperomia Holds The Key To Your Lush Indoor Oasis Forever 📰 This Overlooked Tool Youll Never Want To Live Without 📰 This Overlooked Trick In Ovaltine Makes All The Difference 📰 This Oversized Chair Will Blow Your Mindno Seat Too Big 📰 This Owls Eerie Silence Hides Feathers Gonesomething Utterly Unforgettable 📰 This Oxford Shirt Hides Secrets That Make You The Most Stylish Guest Always 📰 This Oxtail Secret Is Spreading Fastfound Right Near You 📰 This Oxy Contact Secrets Change How You Use Every Drop Forever 📰 This Oz 750Ml Elixir Holds The Secret To Unstoppable Energy Every Single Day 📰 This Oz Litre Claims Powers That Will Change Everythingexperience Oz Litri 📰 This P Oren Lifestyle Cuts Through The Noise Like A Blade

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.