\Rightarrow (x^2 + y^2 + z^2) - 2x - 2z + 2 = 2

Optimize Your Equation: Solve and Simplify » (𝑥² + likewise for y² + z²) – A Step-by-Step Guide

If you’ve ever come across the equation  (𝑥² + y² + z²) – 2𝑥 – 2𝑧 + 2 = 2, you're not alone. This mathematical expression combines algebraic manipulation and geometric interpretation, making it a great example for learners, students, and anyone exploring quadratic surfaces. Today, we’ll break down how to simplify and interpret this equation — turning it into a clearer, actionable form.

Understanding the Context

Understanding the Equation

The given equation is:

(𝑥² + y² + z²) – 2𝑥 – 2z + 2 = 2

At first glance, it’s a quadratic in three variables, but notice how several terms resemble the expansion of a squared binomial. This realization is key to simplifying and solving it.

$\Rightarrow (x^2 + y^2 + z^2) - 2x - 2z + 2 = 2$

Key Insights

Step 1: Simplify Both Sides

Subtract 2 from both sides to simplify:

(𝑥² + y² + z²) – 2𝑥 – 2z + 2 – 2 = 0

Simplify:

𝑥² + y² + z² – 2𝑥 – 2z = 0

🔗 Related Articles You Might Like:

📰 Pink Eye At Home? Here’s What Happens If Someone Contaminates Your Space 📰 Shocking Truth: Pink Eye Is More Contagious Than You Think—I Saw It Firsthand 📰 If You Touch Something With Pink Eye, This Is How Fast It Spreads—don’t panic! 📰 From Miku To Mk The Ultimate Deep Dive Into The Most Hyped Characters Ever 📰 From Miracles To Betrayalsmr Church The Movie Shocks Every Faith Fan Forever 📰 From Monkeys To Myth The Mysterious White Monkey Taking Over Feeds 📰 From Moria To One Piece Madness This Fan Theory Will Blow Your Mind 📰 From Mortal Commands To Comic Capesheres Why Mortal Kombat Crushes Dc In Fan Fights 📰 From Mud To Glory The Dark Hidden Truths Behind Mudding Movies You Missed 📰 From Mud To Glory The Muddy Buddy Formula That Wont Fail 📰 From My Love Notes In Italian To My Souls Songwatch How Love Shines Through 📰 From Mystery To Magic Moelliers Surprising Benefits You Must Try Today 📰 From Myth To Garden The Amazing Power Of This Enchanted Egg You Must Try 📰 From Myth To Myth Busting The True Story Of Mon Calamaris Amazing Abilities 📰 From Myth To Reality The Full Story Of Morristyg That Will Change How You See It 📰 From Naked To Unstoppable The Breakthrough Moments Of Naked Brothers Bands Wild Live Show 📰 From Near Total Collapse To Championship Glory Mt St Helens Before And After That Shocked Fans 📰 From Next To Nothing To Cultural Phenomenon The All Time Bestseller You Need To Know

Final Thoughts

Step 2: Complete the Square

Group the terms involving 𝑥 and z to complete the square:

For 𝑥² – 2𝑥:
𝑥² – 2𝑥 = (𝑥 – 1)² – 1
For z² – 2z:
z² – 2z = (z – 1)² – 1

Now substitute back:

(𝑥 – 1)² – 1 + y² + (z – 1)² – 1 = 0

Combine constants:

(𝑥 – 1)² + y² + (z – 1)² – 2 = 0

Move constant to the right:

(𝑥 – 1)² + y² + (z – 1)² = 2