Expanding, x² + 2x + 1 - x² = 35, so 2x + 1 = 35. - Treasure Valley Movers

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

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.

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Step 1: Simplify the Equation by Expanding

The original equation is:

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

Though it looks simpler now, understanding that this follows from expanding (and canceling) the original expression is key to mastering algebraic simplification.

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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.

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Step 3: Solve for x