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 3x^2 + 5x - 28 = 0. Include step-by-step reasoning in your response. Assistant 1's response: Sure, I can help you solve for x in this equation. Here are the steps: 1. Begin by applying the quadratic formula: x = (-b ± sqrt(b²-4ac)) / 2a 2. Plug in the values of a, b, and c from the equation: a = 3, b = 5, and c = -28 3. Calculate the discriminant (b²-4ac): (5²-4 x 3 x -28) = 25-16 = 9 4. Use the quadratic formula with the calculated discriminant: x = (-(5 ± sqrt(9)) / 3) 5. Simplify the expression: x = (-5 ± sqrt(9)) / 3 6. Find the two possible values for x: x = 5 or x = 2 7. Check each value by plugging it back into the original equation: - When x = 5, the equation becomes 3(5)^2 + 5(5) - 28 = 0, which simplifies to 125 + 25 - 28 = 0, which simplifies to true. - When x = 2, the equation becomes 3(2)^2 + 5(2) - 28 = 0, which simplifies to 16 + 10 - 28 = -12, which simplifies to false. 8. Therefore, the only solution for x is x = 5. I hope this helps! Let me know if you have any further questions or if there's anything else I can assist you with. Assistant 2's response: To solve for x in the quadratic equation 3x^2 + 5x - 28 = 0, we can use the quadratic formula: x = (-b ± sqrt(b^2 - 4ac)) / 2a First, we need to identify a, b, and c in the equation. In this case, a is 3, b is 5, and c is -28. Substituting these values into the quadratic formula, we get: x = (-5 ± sqrt(5^2 - 4(3)(-28))) / 2(3) Simplifying: x = (-5 ± sqrt(25 + 336)) / 6 x = (-5 ± sqrt(361)) / 6 x = (-5 ± 19) / 6 So x can be either (-5 + 19) / 6 or (-5 - 19) / 6: x = 14 / 6 or x = -24 / 6 Simplifying further: x = 7/3 or x = -4 Therefore, the solutions to the quadratic equation 3x^2 + 5x - 28 = 0 are x = 7/3 and x = -4. Assistant 3's response: Sure, we can solve for x in the equation 3x^2 + 5x - 28 = 0. Here's the step-by-step reasoning: 1. Start by identifying the equation's coefficients and constants: 3, 5, and -28. 2. Factor the equation: 3x^2 + 5x - 28 = 0 3x^2 + 5x - 28 = 0 Factoring gives: (3x^2 + 5x) - 28 = 0 = (3x(x + 5)) - 28 = 0 4. Solve for x: x = (-5 ± √(5^2 - 4(3)(-28))) / (2(3)) = (-5 ± √(25 + 112)) / 6 = (-5 ± √37) / 6 = (-5 + 5 √37) / 6 and (-5 - 5 √37) / 6 5. The solutions for x are: x1 = (-5 + 5 √37) / 6 ≈ 2.28 and x2 = (-5 - 5 √37) / 6 ≈ 0.42 Therefore, the solutions for x in the equation 3x^2 + 5x - 28 = 0 are x1 ≈ 2.28 and x2 ≈ 0.42. Assistant 4's response: To solve for x in the equation 3x^2 + 5x - 28 = 0, we first need to isolate the variable x on one side of the equation. We can do this by adding 28 to both sides of the equation: 3x^2 + 5x + 28 = 0 + 28 3x^2 + 5x = 28 Next, we need to find the value of x that makes the equation true. We can use the quadratic formula for this: x = (-b ± sqrt(b^2 - 4ac)) / 2a Here, a = 3, b = 5, and c = 28. Plugging these values into the quadratic formula, we get: x = (-5 ± sqrt(5^2 - 4(3)(28))) / 2(3) x = (-5 ± sqrt(125 - 344)) / 6 x = (-5 ± sqrt(81)) / 6 x = (-5 ± 9) / 6 x = (-5 + 9) / 6 or x = (-5 - 9) / 6 x = -5 / 6 or x = 4 / 6 Therefore, the solution to the equation 3x^2 + 5x - 28 = 0 is either x = -5 / 6 or x = 4 / 6. Assistant 5's response: To solve for x in the equation 3x^2 + 5x - 28 = 0, we can use the quadratic formula: x = (-b ± sqrt(b^2 - 4ac)) / (2a) In this case, a = 3, b = 5, and c = -28. Plugging these values into the formula, we get: x = (5 ± sqrt(5^2 - 4 \* 3 \* -28)) / (2 \* 3) Simplifying, we get: x = (5 ± sqrt(100 + 84)) / 6 x = (5 ± sqrt(184)) / 6 x = (5 ± 13.6) / 6 x = (5 ± 2.17) / 6 x = 5 ± 2.17 / 6 x = 5 ± 0.36 Therefore, the solutions for x are x = 5 + 0.36 and x = 5 - 0.36. Note that because the equation is a quadratic, there are two solutions, and both must be used to find the values of x that satisfy the equation. Assistant 6's response: To solve for x in the equation 3x^2 + 5x - 28 = 0, we can use the quadratic formula: x = (-b ± sqrt(b^2 - 4ac)) / 2a where a = 3, b = 5, and c = -28. First, we need to find the values of a, b, and c in the equation. a = 3 b = 5 c = -28 Next, we substitute these values into the quadratic formula and solve for x. x = (-5 ± sqrt(5^2 - 4(3)(-28))) / 2(3) Simplifying the expression: x = (-5 ± sqrt(448)) / 6 x = (-5 ± 2sqrt(22)) / 6 x = (-5 ± 1.118) / 6 x = (-5 + 1.118) / 6 or (-5 - 1.118) / 6 Therefore, the solutions to the equation 3x^2 + 5x - 28 = 0 are: x = (-5 + 1.118) / 6 or x = (-5 - 1.118) / 6