Expanding, x² + 2x + 1 - x² = 35, so 2x + 1 = 35. - Appfinity Technologies
Expanding the Equation: How to Solve x² + 2x + 1 – x² = 35 Step-by-Step
Expanding the Equation: How to Solve x² + 2x + 1 – x² = 35 Step-by-Step
Misunderstanding algebraic equations can lead to frustration, especially when they appear too simple but require careful expansion. One common but tricky equation is:
x² + 2x + 1 – x² = 35
Understanding the Context
At first glance, the x² terms seem confusing, but with proper expansion and simplification, solving for x becomes straightforward. In this article, we’ll explore how expanding this equation step-by-step reveals that 2x + 1 = 35, leading directly to a clear solution.
Step 1: Simplify the Equation by Expanding
The original equation is:
Key Insights
x² + 2x + 1 – x² = 35
Begin by identifying and removing redundant terms. Notice that +x² and –x² cancel out immediately:
(x² – x²) + 2x + 1 = 35
This simplifies to:
2x + 1 = 35
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📰 Question: Two research teams are analyzing plant species across different continents. One team analyzes data from 48 regions, and the other from 72 regions. What is the largest number of regions that could be in each group if they want to divide both datasets into groups of equal size without any regions left out? 📰 Solution: To divide both 48 and 72 regions into equal-sized groups with no regions left out, we must find the greatest common divisor (GCD) of 48 and 72. 📰 We use prime factorization:Final Thoughts
Though it looks simpler now, understanding that this follows from expanding (and canceling) the original expression is key to mastering algebraic simplification.
Step 2: Isolate the Variable
Now that we have 2x + 1 = 35, the next step is to isolate x. Start by subtracting 1 from both sides:
2x + 1 – 1 = 35 – 1
Which simplifies to:
2x = 34
This transformation confirms how subtracting related terms directly leads to a linear equation — a crucial step before solving for x.
