-3634=1111t-49t^2 eching

$$- 3634 = 1111 t - 49 t ^ { 2 }$$

t uchun yechish

$$t = \frac{\sqrt{1946585} + 1111}{98} \approx 25,573476555$$

$$t=\frac{1111-\sqrt{1946585}}{98}\approx -2,900007167$$

Kvadrat tenglamalaridan foydalanish qoidalari

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$1111t-49t^{2}=-3634$$

3634 ni ikki tarafga qo’shing.

$$1111t-49t^{2}+3634=0$$

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.

$$-49t^{2}+1111t+3634=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -49 ni a, 1111 ni b va 3634 ni c bilan almashtiring.

$$t=\frac{-1111±\sqrt{1111^{2}-4\left(-49\right)\times 3634}}{2\left(-49\right)}$$

1111 kvadratini chiqarish.

$$t=\frac{-1111±\sqrt{1234321-4\left(-49\right)\times 3634}}{2\left(-49\right)}$$

-4 ni -49 marotabaga ko'paytirish.

$$t=\frac{-1111±\sqrt{1234321+196\times 3634}}{2\left(-49\right)}$$

196 ni 3634 marotabaga ko'paytirish.

$$t=\frac{-1111±\sqrt{1234321+712264}}{2\left(-49\right)}$$

1234321 ni 712264 ga qo'shish.

$$t=\frac{-1111±\sqrt{1946585}}{2\left(-49\right)}$$

2 ni -49 marotabaga ko'paytirish.

$$t=\frac{-1111±\sqrt{1946585}}{-98}$$

t=\frac{-1111±\sqrt{1946585}}{-98} tenglamasini yeching, bunda ± musbat. -1111 ni \sqrt{1946585} ga qo'shish.

$$t=\frac{\sqrt{1946585}-1111}{-98}$$

-1111+\sqrt{1946585} ni -98 ga bo'lish.

$$t=\frac{1111-\sqrt{1946585}}{98}$$

t=\frac{-1111±\sqrt{1946585}}{-98} tenglamasini yeching, bunda ± manfiy. -1111 dan \sqrt{1946585} ni ayirish.

$$t=\frac{-\sqrt{1946585}-1111}{-98}$$

-1111-\sqrt{1946585} ni -98 ga bo'lish.

$$t=\frac{\sqrt{1946585}+1111}{98}$$

Tenglama yechildi.

$$t=\frac{1111-\sqrt{1946585}}{98} t=\frac{\sqrt{1946585}+1111}{98}$$

Kvadratni yakunlash bo'yicha qadamlar

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$1111t-49t^{2}=-3634$$

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

$$-49t^{2}+1111t=-3634$$

Ikki tarafini -49 ga bo‘ling.

$$\frac{-49t^{2}+1111t}{-49}=-\frac{3634}{-49}$$

-49 ga bo'lish -49 ga ko'paytirishni bekor qiladi.

$$t^{2}+\frac{1111}{-49}t=-\frac{3634}{-49}$$

1111 ni -49 ga bo'lish.

$$t^{2}-\frac{1111}{49}t=-\frac{3634}{-49}$$

-3634 ni -49 ga bo'lish.

$$t^{2}-\frac{1111}{49}t=\frac{3634}{49}$$

-\frac{1111}{49} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{1111}{98} olish uchun. Keyin, -\frac{1111}{98} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$t^{2}-\frac{1111}{49}t+\left(-\frac{1111}{98}\right)^{2}=\frac{3634}{49}+\left(-\frac{1111}{98}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{1111}{98} kvadratini chiqarish.

$$t^{2}-\frac{1111}{49}t+\frac{1234321}{9604}=\frac{3634}{49}+\frac{1234321}{9604}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{3634}{49} ni \frac{1234321}{9604} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$t^{2}-\frac{1111}{49}t+\frac{1234321}{9604}=\frac{1946585}{9604}$$

t^{2}-\frac{1111}{49}t+\frac{1234321}{9604} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(t-\frac{1111}{98}\right)^{2}=\frac{1946585}{9604}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(t-\frac{1111}{98}\right)^{2}}=\sqrt{\frac{1946585}{9604}}$$

Qisqartirish.

$$t-\frac{1111}{98}=\frac{\sqrt{1946585}}{98} t-\frac{1111}{98}=-\frac{\sqrt{1946585}}{98}$$

\frac{1111}{98} ni tenglamaning ikkala tarafiga qo'shish.

$$t=\frac{\sqrt{1946585}+1111}{98} t=\frac{1111-\sqrt{1946585}}{98}$$