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:

📰 Ways to Make Tires Shine Like New Without the Store Price 📰 Shine So Bright Everyone Will Ask What You’re Using 📰 The Hidden Layer That Turns Dull Rubber Into Wheel Magic 📰 Parcours Politique 📰 Parents Dream Muslim Boy Names Enroll Your Son Today 📰 Part Chicken Jockey Chopped Medias Epic Minecraft Movie You Need To See 📰 Passwords Blocked Due To Policy Compliance 📰 Peacock Just Dropped A Movie Treasure Hunt Watch These Edge Of Your Seat Films Tonight 📰 Peacocks Secret Movie Vault 5 Hidden Gems You Cant Miss Right Now 📰 Peak Emotional Breakdown All Movies With Paul Walker You Must Watch Before He Went Forever 📰 Pendant 3 Heures 72 Mph La Voiture Parcourt 3 72 Miles 216 Miles 📰 People Are Obsessed With Mutowhat This Star Isnt Saying Could Shock You 📰 Perdi El 15 De 32 015 32 015324848 Que Se Redondea A 5 Canicas Perdidas Si Se Redondean A Nmeros Enteros 📰 Perfect For Every Occasion Discover The Modest Dresses That Are Hiring Every Closet 📰 Perfect Mini Bundt Cakes For Every Occasion See Why Bakers Cant Resist 📰 Perfect Mini Meatloaf Recipe Thats Smaller But Massive On Flavor 📰 Perhaps Completes 720 Refers To Tracking Accuracy Or Data Points But For Math We Take It As Literal Minute Gear Rotates 720 Times In 24 Hours 📰 Perhaps In This Exhibit The Minute Hand Makes 720 Rotations In 24 Hours Impossible

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.