{"generator":"equations.quadratic","version":1,"value":{"problems":[{"prompt":"4x^2 - 4x - 80 = 0","prompt_latex":"4x^{2} - 4x - 80 = 0","answer":"x = -4  or  x = 5","answer_latex":"x = -4  or  x = 5","factored":"4(x - 5)(x + 4)"},{"prompt":"3x^2 + 42x + 135 = 0","prompt_latex":"3x^{2} + 42x + 135 = 0","answer":"x = -9  or  x = -5","answer_latex":"x = -9  or  x = -5","factored":"3(x + 5)(x + 9)"},{"prompt":"-2x^2 + 18x - 28 = 0","prompt_latex":"-2x^{2} + 18x - 28 = 0","answer":"x = 2  or  x = 7","answer_latex":"x = 2  or  x = 7","factored":"-2(x - 2)(x - 7)"},{"prompt":"-2x^2 + 14x - 20 = 0","prompt_latex":"-2x^{2} + 14x - 20 = 0","answer":"x = 2  or  x = 5","answer_latex":"x = 2  or  x = 5","factored":"-2(x - 2)(x - 5)"},{"prompt":"-x^2 - 7x + 18 = 0","prompt_latex":"-x^{2} - 7x + 18 = 0","answer":"x = -9  or  x = 2","answer_latex":"x = -9  or  x = 2","factored":"-(x - 2)(x + 9)"},{"prompt":"4x^2 + 12x = 0","prompt_latex":"4x^{2} + 12x = 0","answer":"x = -3  or  x = 0","answer_latex":"x = -3  or  x = 0","factored":"4x(x + 3)"}],"count":6},"display":"1. 4x^2 - 4x - 80 = 0   \u2192   x = -4  or  x = 5\n2. 3x^2 + 42x + 135 = 0   \u2192   x = -9  or  x = -5\n3. -2x^2 + 18x - 28 = 0   \u2192   x = 2  or  x = 7\n4. -2x^2 + 14x - 20 = 0   \u2192   x = 2  or  x = 5\n5. -x^2 - 7x + 18 = 0   \u2192   x = -9  or  x = 2\n6. 4x^2 + 12x = 0   \u2192   x = -3  or  x = 0","meta":{"latex":[["4x^{2} - 4x - 80 = 0","x = -4  or  x = 5"],["3x^{2} + 42x + 135 = 0","x = -9  or  x = -5"],["-2x^{2} + 18x - 28 = 0","x = 2  or  x = 7"],["-2x^{2} + 14x - 20 = 0","x = 2  or  x = 5"],["-x^{2} - 7x + 18 = 0","x = -9  or  x = 2"],["4x^{2} + 12x = 0","x = -3  or  x = 0"]],"problems":6,"stream_bytes_used":30,"rejections":12,"entropy_in_bytes":16,"duration_us":788},"receipt":{"source":"drand","source_label":"drand \u00b7 League of Entropy","class":"B","class_label":"Public beacon","caveat":"Published openly \u2014 anyone can look this value up after the fact.","narrative":"drand round 6,463,216 \u2014 no single operator could have predicted this value.","proof_url":"https:\/\/api.drand.sh\/public\/6463216","reference":"6463216","observed_at":"2026-09-13T19:25:13+00:00","degraded":false,"mixed_with_csprng":true,"latency_ms":367,"cached":false},"seed":{"token":"J76FTEM0TWTYWDSYKCHTVMXPQ0","permalink":"https:\/\/randomly.cluxnei.dev\/r\/J76FTEM0TWTYWDSYKCHTVMXPQ0?g=equations.quadratic&v=1&p=eyJjb3VudCI6NiwibW9uaWMiOmZhbHNlLCJyb290cyI6ImludGVnZXIifQ&s=drand&r=6463216"},"uses_entropy":true,"reproducible":true}