Expanding, x² + 2x + 1 - x² = 35, so 2x + 1 = 35.
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.
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.
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.
Step 3: Solve for x
Finally, divide both sides by 2:
2x ÷ 2 = 34 ÷ 2
Thus:
x = 17
Why This Expansion Matters
Even though the expanded form — 2x + 1 = 35 — appears less complex, recognizing it came from expanding the original quadratic expression helps sharpen problem-solving skills. Mastering these steps makes it easier to approach identical equations that may look more complicated with coefficients and constants.
Summary
- Original equation: x² + 2x + 1 – x² = 35
- Expand: (x² – x²) + 2x + 1 = 35 → 2x + 1 = 35
- Subtract 1: 2x = 34
- Divide by 2: x = 17
By systematically expanding and simplifying, solving algebraic expressions becomes intuitive and confident.
Pro Tips for Solving Similar Equations
- Watch for redundancies like x² – x² that cancel out.
- Always isolate the variable term after simplifying.
- Practice expanding binomials and simplifying step-by-step.
Expanding equations properly isn’t just about mechanics — it’s about building logical thinking that powers success in algebra and beyond.
Key Takeaways:
- Expand and simplify carefully.
- Canceling like terms is essential.
- Isolate variables step-by-step.
- Understand each transformation to deepen your algebra skills.
Start simplifying – your next equation will feel easier!
