Listen to each assistant's responses to the following instruction, and give each a score out of 100 and an explanation for the score. Here are some additional guidelines: * Do not award bonus points. * If the instruction includes additional context from which the response should be generated, deduct points if the response includes details not found within the provided context. * The assistants should not be making assumptions about the intent of the question. * If the instruction asks for results in a specific format, e.g. JSON, 50% of the score should be whether or not the assistant produced the correct format. * Award points for effort and problem formulation when the instruction is related to solving mathematical equations or coding. Respond in format "[assistant number]. [score]/100 - [explanation] Instruction: Solve for x in the equation x^2 - 9x + 20 = 0. Include step-by-step reasoning in your response. Assistant 1's response: To solve for x in the equation x^2 - 9x + 20 = 0, we can use the quadratic formula: x = (-b ± √(b²-4ac)) / 2a where a = 1, b = -9, and c = 20. First, we will simplify the equation: x² - 9x + 20 = 0 x² - 9x = -20 Next, we will substitute a, b, and c into the quadratic formula: x = (-(-9) ± √((-9)²-4(1)(20))) / 2(1) Now, we will calculate the two possible roots: x = (-9 ± √(9+80)) / 2 We can make the calculation easier by noticing that 9+80 = 89, so our square root is √89. x = (-9 ± 8) / 2 Finally, we'll find the two possible roots. The first root is x = -9 + 8 = 17, and the second root is x = -9 - 8 = -17. So, the solutions to the equation x^2 - 9x + 20 = 0 are x = 17 and x = -17. Assistant 2's response: To solve for x in the equation x^2 - 9x + 20 = 0, we can use the quadratic formula: x = (-b ± sqrt(b^2 - 4ac)) / 2a where a, b, and c are the coefficients of the equation: a = 1, b = -9, c = 20 Plugging these values into the formula, we get: x = (-(-9) ± sqrt((-9)^2 - 4(1)(20))) / 2(1) Simplifying the expression within the square root, we get: x = (9 ± sqrt(81 - 80)) / 2 x = (9 ± sqrt(1)) / 2 x = (9 + 1) / 2 or x = (9 - 1) / 2 Simplifying further, we get: x = 5 or x = 4 Therefore, the solutions to the equation x^2 - 9x + 20 = 0 are x = 5 and x = 4. Assistant 3's response: To solve for x in the equation x^2 - 9x + 20 = 0, we can use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a In this case, a = 1, b = -9, and c = 20. Plugging these values into the formula, we get: x = (-(-9) ± √((-9)^2 - 4(1)(20))) / 2(1) x = (9 ± √(81 - 80)) / 2 x = (9 ± √1) / 2 x = (9 ± 1) / 2 This gives us two solutions, x = (9 + 1) / 2 and x = (9 - 1) / 2, which simplify to x = 5 and x = 4, respectively. Therefore, the solutions for the equation x^2 - 9x + 20 = 0 are x = 5 and x = 4. Assistant 4's response: To solve for x in the equation x^2 - 9x + 20 = 0, we can use the quadratic formula, which is ax^2 + bx + c = 0. In this case, a = 1, b = -9, and c = 20. Plugging those values into the quadratic formula, we get: x = (-b ± sqrt(b^2 - 4ac)) / 2a x = (-(-9) ± sqrt((-9)^2 - 4(1)(20))) / 2(1) x = (9 ± sqrt(81 - 80)) / 2 x = (9 ± sqrt(1)) / 2 x = (9 ± 1) / 2 x = 4.5 or x = 5.5 Therefore, x = 5.5 is the solution to the equation x^2 - 9x + 20 = 0. Assistant 5's response: To solve for x in the equation x² - 9x + 20 = 0, we need to use the quadratic formula. The quadratic formula is x = (-b +/- sqrt(b^2 - 4ac)) / 2a. In this case, a = 1, b = -9, and c = 20. Plugging these values into the formula, we get x = (-(-9) +/- sqrt((-9)^2 - 4(1)(20))) / 2(1). Simplifying, we get x = (9 +/- sqrt(81 - 40)) / 2. Finally, we get x = (9 +/- sqrt(41)) / 2. Since the discriminant (b^2 - 4ac) is positive, the solutions are real numbers. The solutions are x = (9 +/- sqrt(41)) / 2. Assistant 6's response: To solve for x in the equation x^2 - 9x + 20 = 0, we can use the quadratic formula: x = (-b ± sqrt(b^2 - 4ac)) / 2a where a = 1, b = -9, and c = 20. First, we need to find the values of a, b, and c: a = 1 b = -9 c = 20 Next, we substitute these values into the quadratic formula: x = (-(-9) ± sqrt((-9)^2 - 4(1)(20))) / 2(1) Simplifying: x = (9 ± sqrt(161)) / 2 x = (9 ± 12.36) / 2 x = 3.64 or 4.96 Therefore, the solutions to the equation x^2 - 9x + 20 = 0 are x = 3.64 and x = 4.96.