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Solve (6x² - 7x - 3) - (5x² - 1 + 2x) - (2x² - 3 + x)

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Final answer:

To solve the polynomial expression, distribute the negative signs across the second and third polynomials and combine like terms, simplifying it to a quadratic equation which can be solved using the quadratic formula.

Step-by-step explanation:

To solve the equation (6x² - 7x - 3) - (5x² - 1 + 2x) - (2x² - 3 + x), you must combine like terms by subtracting the second and third polynomials from the first. Start by distributing the negative sign across the terms in the second and third polynomials:

  • (6x² - 7x - 3) - 5x² + 1 - 2x
  • (6x² - 7x - 3) - 2x² + 3 - x

Next, combine like terms:

  • 6x² - 5x² - 2x² = -x²
  • -7x - 2x + x = -8x
  • -3 + 1 + 3 = 1

Therefore, the simplified equation is -x² - 8x + 1. This result is a quadratic equation and can be solved for x using the quadratic formula:

x = [-b ± √(b² - 4ac)] / (2a)

where in this case a = -1, b = -8, and c = 1. After substitution into the formula, you would solve for the two possible solutions for x. Lastly, check to see if your answers are reasonable.

User Sterling Nichols
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