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.