44t^2-244t=0 eching

$$44 t ^ { 2 } - 244 t = 0$$

t uchun yechish

$$t = \frac{61}{11} = 5\frac{6}{11} \approx 5,545454545$$

$$t=0$$

Faktorlash qadamlari

t omili.

$$t\left(44t-244\right)=0$$

Tenglamani yechish uchun t=0 va 44t-244=0 ni yeching.

$$t=0 t=\frac{61}{11}$$

Kvadrat tenglamalaridan foydalanish qoidalari

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.

$$44t^{2}-244t=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 44 ni a, -244 ni b va 0 ni c bilan almashtiring.

$$t=\frac{-\left(-244\right)±\sqrt{\left(-244\right)^{2}}}{2\times 44}$$

\left(-244\right)^{2} ning kvadrat ildizini chiqarish.

$$t=\frac{-\left(-244\right)±244}{2\times 44}$$

-244 ning teskarisi 244 ga teng.

$$t=\frac{244±244}{2\times 44}$$

2 ni 44 marotabaga ko'paytirish.

$$t=\frac{244±244}{88}$$

t=\frac{244±244}{88} tenglamasini yeching, bunda ± musbat. 244 ni 244 ga qo'shish.

$$t=\frac{488}{88}$$

\frac{488}{88} ulushini 8 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$t=\frac{61}{11}$$

t=\frac{244±244}{88} tenglamasini yeching, bunda ± manfiy. 244 dan 244 ni ayirish.

$$t=\frac{0}{88}$$

0 ni 88 ga bo'lish.

$$t=0$$

Tenglama yechildi.

$$t=\frac{61}{11} t=0$$

Kvadratni yakunlash bo'yicha qadamlar

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

$$44t^{2}-244t=0$$

Ikki tarafini 44 ga bo‘ling.

$$\frac{44t^{2}-244t}{44}=\frac{0}{44}$$

44 ga bo'lish 44 ga ko'paytirishni bekor qiladi.

$$t^{2}+\left(-\frac{244}{44}\right)t=\frac{0}{44}$$

\frac{-244}{44} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$t^{2}-\frac{61}{11}t=\frac{0}{44}$$

0 ni 44 ga bo'lish.

$$t^{2}-\frac{61}{11}t=0$$

-\frac{61}{11} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{61}{22} olish uchun. Keyin, -\frac{61}{22} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$t^{2}-\frac{61}{11}t+\left(-\frac{61}{22}\right)^{2}=\left(-\frac{61}{22}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{61}{22} kvadratini chiqarish.

$$t^{2}-\frac{61}{11}t+\frac{3721}{484}=\frac{3721}{484}$$

t^{2}-\frac{61}{11}t+\frac{3721}{484} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(t-\frac{61}{22}\right)^{2}=\frac{3721}{484}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(t-\frac{61}{22}\right)^{2}}=\sqrt{\frac{3721}{484}}$$

Qisqartirish.

$$t-\frac{61}{22}=\frac{61}{22} t-\frac{61}{22}=-\frac{61}{22}$$

\frac{61}{22} ni tenglamaning ikkala tarafiga qo'shish.

$$t=\frac{61}{11} t=0$$