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12t-5t^{2}=17
Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.
12t-5t^{2}-17=0
Ikkala tarafdan 17 ni ayirish.
-5t^{2}+12t-17=0
ax^{2}+bx+c=0 shaklidagi barcha tenglamalarni kvadrat formulasi bilan yechish mumkin: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadrat formula ikki yechmni taqdim qiladi, biri ± qo'shish bo'lganda, va ikkinchisi ayiruv bo'lganda.
t=\frac{-12±\sqrt{12^{2}-4\left(-5\right)\left(-17\right)}}{2\left(-5\right)}
Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -5 ni a, 12 ni b va -17 ni c bilan almashtiring.
t=\frac{-12±\sqrt{144-4\left(-5\right)\left(-17\right)}}{2\left(-5\right)}
12 kvadratini chiqarish.
t=\frac{-12±\sqrt{144+20\left(-17\right)}}{2\left(-5\right)}
-4 ni -5 marotabaga ko'paytirish.
t=\frac{-12±\sqrt{144-340}}{2\left(-5\right)}
20 ni -17 marotabaga ko'paytirish.
t=\frac{-12±\sqrt{-196}}{2\left(-5\right)}
144 ni -340 ga qo'shish.
t=\frac{-12±14i}{2\left(-5\right)}
-196 ning kvadrat ildizini chiqarish.
t=\frac{-12±14i}{-10}
2 ni -5 marotabaga ko'paytirish.
t=\frac{-12+14i}{-10}
t=\frac{-12±14i}{-10} tenglamasini yeching, bunda ± musbat. -12 ni 14i ga qo'shish.
t=\frac{6}{5}-\frac{7}{5}i
-12+14i ni -10 ga bo'lish.
t=\frac{-12-14i}{-10}
t=\frac{-12±14i}{-10} tenglamasini yeching, bunda ± manfiy. -12 dan 14i ni ayirish.
t=\frac{6}{5}+\frac{7}{5}i
-12-14i ni -10 ga bo'lish.
t=\frac{6}{5}-\frac{7}{5}i t=\frac{6}{5}+\frac{7}{5}i
Tenglama yechildi.
12t-5t^{2}=17
Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.
-5t^{2}+12t=17
Bu kabi kvadrat tenglamalarni kvadratni yakunlab yechish mumkin. Kvadratni yechish uchun tenglama avval ushbu shaklda bo'lishi shart: x^{2}+bx=c.
\frac{-5t^{2}+12t}{-5}=\frac{17}{-5}
Ikki tarafini -5 ga bo‘ling.
t^{2}+\frac{12}{-5}t=\frac{17}{-5}
-5 ga bo'lish -5 ga ko'paytirishni bekor qiladi.
t^{2}-\frac{12}{5}t=\frac{17}{-5}
12 ni -5 ga bo'lish.
t^{2}-\frac{12}{5}t=-\frac{17}{5}
17 ni -5 ga bo'lish.
t^{2}-\frac{12}{5}t+\left(-\frac{6}{5}\right)^{2}=-\frac{17}{5}+\left(-\frac{6}{5}\right)^{2}
-\frac{12}{5} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{6}{5} olish uchun. Keyin, -\frac{6}{5} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.
t^{2}-\frac{12}{5}t+\frac{36}{25}=-\frac{17}{5}+\frac{36}{25}
Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{6}{5} kvadratini chiqarish.
t^{2}-\frac{12}{5}t+\frac{36}{25}=-\frac{49}{25}
Umumiy maxrajni topib va hisoblovchini qo'shish orqali -\frac{17}{5} ni \frac{36}{25} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.
\left(t-\frac{6}{5}\right)^{2}=-\frac{49}{25}
t^{2}-\frac{12}{5}t+\frac{36}{25} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.
\sqrt{\left(t-\frac{6}{5}\right)^{2}}=\sqrt{-\frac{49}{25}}
Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.
t-\frac{6}{5}=\frac{7}{5}i t-\frac{6}{5}=-\frac{7}{5}i
Qisqartirish.
t=\frac{6}{5}+\frac{7}{5}i t=\frac{6}{5}-\frac{7}{5}i
\frac{6}{5} ni tenglamaning ikkala tarafiga qo'shish.