11(1)=-10t^2+44t+30 eching

$$11 ( 1 ) = - 10 t ^ { 2 } + 44 t + 30$$

t uchun yechish

$$t=\frac{\sqrt{674}}{10}+\frac{11}{5}\approx 4,796150997$$

$$t=-\frac{\sqrt{674}}{10}+\frac{11}{5}\approx -0,396150997$$

Kvadrat tenglamalaridan foydalanish qoidalari

11 hosil qilish uchun 11 va 1 ni ko'paytirish.

$$11=-10t^{2}+44t+30$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$-10t^{2}+44t+30=11$$

Ikkala tarafdan 11 ni ayirish.

$$-10t^{2}+44t+30-11=0$$

19 olish uchun 30 dan 11 ni ayirish.

$$-10t^{2}+44t+19=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -10 ni a, 44 ni b va 19 ni c bilan almashtiring.

$$t=\frac{-44±\sqrt{44^{2}-4\left(-10\right)\times 19}}{2\left(-10\right)}$$

44 kvadratini chiqarish.

$$t=\frac{-44±\sqrt{1936-4\left(-10\right)\times 19}}{2\left(-10\right)}$$

-4 ni -10 marotabaga ko'paytirish.

$$t=\frac{-44±\sqrt{1936+40\times 19}}{2\left(-10\right)}$$

40 ni 19 marotabaga ko'paytirish.

$$t=\frac{-44±\sqrt{1936+760}}{2\left(-10\right)}$$

1936 ni 760 ga qo'shish.

$$t=\frac{-44±\sqrt{2696}}{2\left(-10\right)}$$

2696 ning kvadrat ildizini chiqarish.

$$t=\frac{-44±2\sqrt{674}}{2\left(-10\right)}$$

2 ni -10 marotabaga ko'paytirish.

$$t=\frac{-44±2\sqrt{674}}{-20}$$

t=\frac{-44±2\sqrt{674}}{-20} tenglamasini yeching, bunda ± musbat. -44 ni 2\sqrt{674} ga qo'shish.

$$t=\frac{2\sqrt{674}-44}{-20}$$

-44+2\sqrt{674} ni -20 ga bo'lish.

$$t=-\frac{\sqrt{674}}{10}+\frac{11}{5}$$

t=\frac{-44±2\sqrt{674}}{-20} tenglamasini yeching, bunda ± manfiy. -44 dan 2\sqrt{674} ni ayirish.

$$t=\frac{-2\sqrt{674}-44}{-20}$$

-44-2\sqrt{674} ni -20 ga bo'lish.

$$t=\frac{\sqrt{674}}{10}+\frac{11}{5}$$

Tenglama yechildi.

$$t=-\frac{\sqrt{674}}{10}+\frac{11}{5} t=\frac{\sqrt{674}}{10}+\frac{11}{5}$$

Kvadratni yakunlash bo'yicha qadamlar

11 hosil qilish uchun 11 va 1 ni ko'paytirish.

$$11=-10t^{2}+44t+30$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$-10t^{2}+44t+30=11$$

Ikkala tarafdan 30 ni ayirish.

$$-10t^{2}+44t=11-30$$

-19 olish uchun 11 dan 30 ni ayirish.

$$-10t^{2}+44t=-19$$

Ikki tarafini -10 ga bo‘ling.

$$\frac{-10t^{2}+44t}{-10}=-\frac{19}{-10}$$

-10 ga bo'lish -10 ga ko'paytirishni bekor qiladi.

$$t^{2}+\frac{44}{-10}t=-\frac{19}{-10}$$

\frac{44}{-10} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$t^{2}-\frac{22}{5}t=-\frac{19}{-10}$$

-19 ni -10 ga bo'lish.

$$t^{2}-\frac{22}{5}t=\frac{19}{10}$$

-\frac{22}{5} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{11}{5} olish uchun. Keyin, -\frac{11}{5} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$t^{2}-\frac{22}{5}t+\left(-\frac{11}{5}\right)^{2}=\frac{19}{10}+\left(-\frac{11}{5}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{11}{5} kvadratini chiqarish.

$$t^{2}-\frac{22}{5}t+\frac{121}{25}=\frac{19}{10}+\frac{121}{25}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{19}{10} ni \frac{121}{25} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$t^{2}-\frac{22}{5}t+\frac{121}{25}=\frac{337}{50}$$

t^{2}-\frac{22}{5}t+\frac{121}{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.

$$\left(t-\frac{11}{5}\right)^{2}=\frac{337}{50}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(t-\frac{11}{5}\right)^{2}}=\sqrt{\frac{337}{50}}$$

Qisqartirish.

$$t-\frac{11}{5}=\frac{\sqrt{674}}{10} t-\frac{11}{5}=-\frac{\sqrt{674}}{10}$$

\frac{11}{5} ni tenglamaning ikkala tarafiga qo'shish.

$$t=\frac{\sqrt{674}}{10}+\frac{11}{5} t=-\frac{\sqrt{674}}{10}+\frac{11}{5}$$