Final answer:
Equations A) 4x² - 11x = 7, B) 5x² = 3x, C) (x + 3)(x - 2) = 1, and D) (x - 7)² + 3 = 0 are written in standard form and the values for a, b, and c are identified for each, allowing for the use of the quadratic formula to solve for x.
Step-by-step explanation:
Here's how we can write the given equations in standard form and identify the values of a, b, and c: 4x² - 11x = 7: To get it in standard form, you subtract 7 from both sides, resulting in 4x² - 11x - 7 = 0. Here, a = 4, b = -11, and c = -7. 5x² = 3x: You would subtract 3x from both sides to get 5x² - 3x = 0. For this equation, a = 5, b = -3, and c = 0. (x + 3)(x - 2) = 1: If you expand this, you get x² - 2x + 3x - 6 = 1, which simplifies to x² + x - 6 = 1. Then, subtracting 1 from both sides, you have x² + x - 7 = 0. In this case, a = 1, b = 1, and c = -7. (x - 7)² + 3 = 0: First, you would expand the binomial to get x² - 14x + 49 + 3 = 0, and then combine the constant terms: x² - 14x + 52 = 0. Here, a = 1, b = -14, and c = 52. To solve these equations for x, you could use the quadratic formula which is x = [-b ± √(b² - 4ac)] / (2a).