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(x-2)^2+x^2 2x^2-3x-5

2 min read Jun 17, 2024
(x-2)^2+x^2 2x^2-3x-5

Simplifying and Solving the Expression: (x-2)² + x² = 2x² - 3x - 5

This article will explore the simplification and potential solutions for the given expression: (x-2)² + x² = 2x² - 3x - 5.

Simplifying the Expression

  1. Expand the square: (x-2)² = (x-2)(x-2) = x² - 4x + 4
  2. Combine like terms: The expression becomes: x² - 4x + 4 + x² = 2x² - 3x - 5
  3. Rearrange: 2x² - 4x + 4 = 2x² - 3x - 5
  4. Move all terms to one side: -4x + 4 + 3x + 5 = 0
  5. Simplify: -x + 9 = 0

Solving for x

Now we have a simple linear equation: -x + 9 = 0.

  1. Isolate x: x = 9

Therefore, the solution to the expression (x-2)² + x² = 2x² - 3x - 5 is x = 9.

Conclusion

By simplifying and rearranging the expression, we arrived at a linear equation. Solving for x reveals that the only solution is x = 9. It's important to note that this solution satisfies the original expression, making it a valid solution.

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