6t+35t^2/2=12 eching

$$6t+ \frac{ 35 { t }^{ 2 } }{ 2 } = 12$$

t uchun yechish

$$t=\frac{2\sqrt{219}-6}{35}\approx 0,674208491$$

$$t=\frac{-2\sqrt{219}-6}{35}\approx -1,017065634$$

Kvadrat tenglamalaridan foydalanish qoidalari

Tenglamaning ikkala tarafini 2 ga ko'paytirish.

$$12t+35t^{2}=24$$

Ikkala tarafdan 24 ni ayirish.

$$12t+35t^{2}-24=0$$

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.

$$35t^{2}+12t-24=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 35 ni a, 12 ni b va -24 ni c bilan almashtiring.

$$t=\frac{-12±\sqrt{12^{2}-4\times 35\left(-24\right)}}{2\times 35}$$

12 kvadratini chiqarish.

$$t=\frac{-12±\sqrt{144-4\times 35\left(-24\right)}}{2\times 35}$$

-4 ni 35 marotabaga ko'paytirish.

$$t=\frac{-12±\sqrt{144-140\left(-24\right)}}{2\times 35}$$

-140 ni -24 marotabaga ko'paytirish.

$$t=\frac{-12±\sqrt{144+3360}}{2\times 35}$$

144 ni 3360 ga qo'shish.

$$t=\frac{-12±\sqrt{3504}}{2\times 35}$$

3504 ning kvadrat ildizini chiqarish.

$$t=\frac{-12±4\sqrt{219}}{2\times 35}$$

2 ni 35 marotabaga ko'paytirish.

$$t=\frac{-12±4\sqrt{219}}{70}$$

t=\frac{-12±4\sqrt{219}}{70} tenglamasini yeching, bunda ± musbat. -12 ni 4\sqrt{219} ga qo'shish.

$$t=\frac{4\sqrt{219}-12}{70}$$

-12+4\sqrt{219} ni 70 ga bo'lish.

$$t=\frac{2\sqrt{219}-6}{35}$$

t=\frac{-12±4\sqrt{219}}{70} tenglamasini yeching, bunda ± manfiy. -12 dan 4\sqrt{219} ni ayirish.

$$t=\frac{-4\sqrt{219}-12}{70}$$

-12-4\sqrt{219} ni 70 ga bo'lish.

$$t=\frac{-2\sqrt{219}-6}{35}$$

Tenglama yechildi.

$$t=\frac{2\sqrt{219}-6}{35} t=\frac{-2\sqrt{219}-6}{35}$$

Kvadratni yakunlash bo'yicha qadamlar

Tenglamaning ikkala tarafini 2 ga ko'paytirish.

$$12t+35t^{2}=24$$

Bu kabi kvadrat tenglamalarni kvadratni yakunlab yechish mumkin. Kvadratni yechish uchun tenglama avval ushbu shaklda bo'lishi shart: x^{2}+bx=c.

$$35t^{2}+12t=24$$

Ikki tarafini 35 ga bo‘ling.

$$\frac{35t^{2}+12t}{35}=\frac{24}{35}$$

35 ga bo'lish 35 ga ko'paytirishni bekor qiladi.

$$t^{2}+\frac{12}{35}t=\frac{24}{35}$$

\frac{12}{35} ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{6}{35} olish uchun. Keyin, \frac{6}{35} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$t^{2}+\frac{12}{35}t+\left(\frac{6}{35}\right)^{2}=\frac{24}{35}+\left(\frac{6}{35}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{6}{35} kvadratini chiqarish.

$$t^{2}+\frac{12}{35}t+\frac{36}{1225}=\frac{24}{35}+\frac{36}{1225}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{24}{35} ni \frac{36}{1225} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$t^{2}+\frac{12}{35}t+\frac{36}{1225}=\frac{876}{1225}$$

t^{2}+\frac{12}{35}t+\frac{36}{1225} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(t+\frac{6}{35}\right)^{2}=\frac{876}{1225}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(t+\frac{6}{35}\right)^{2}}=\sqrt{\frac{876}{1225}}$$

Qisqartirish.

$$t+\frac{6}{35}=\frac{2\sqrt{219}}{35} t+\frac{6}{35}=-\frac{2\sqrt{219}}{35}$$

Tenglamaning ikkala tarafidan \frac{6}{35} ni ayirish.

$$t=\frac{2\sqrt{219}-6}{35} t=\frac{-2\sqrt{219}-6}{35}$$