3782x^2+165735x+91*10^6=0 eching

$$3782 x ^ { 2 } + 165735 x + 91 \times 10 ^ { 6 } = 0$$

x uchun yechish (complex solution)

$$x=\frac{-165735+5\sqrt{53967196391}i}{7564}\approx -21,911025912+153,561877262i$$

$$x=\frac{-5\sqrt{53967196391}i-165735}{7564}\approx -21,911025912-153,561877262i$$

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.

$$3782x^{2}+165735x+91000000=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 3782 ni a, 165735 ni b va 91000000 ni c bilan almashtiring.

$$x=\frac{-165735±\sqrt{165735^{2}-4\times 3782\times 91000000}}{2\times 3782}$$

165735 kvadratini chiqarish.

$$x=\frac{-165735±\sqrt{27468090225-4\times 3782\times 91000000}}{2\times 3782}$$

-4 ni 3782 marotabaga ko'paytirish.

$$x=\frac{-165735±\sqrt{27468090225-15128\times 91000000}}{2\times 3782}$$

-15128 ni 91000000 marotabaga ko'paytirish.

$$x=\frac{-165735±\sqrt{27468090225-1376648000000}}{2\times 3782}$$

27468090225 ni -1376648000000 ga qo'shish.

$$x=\frac{-165735±\sqrt{-1349179909775}}{2\times 3782}$$

-1349179909775 ning kvadrat ildizini chiqarish.

$$x=\frac{-165735±5\sqrt{53967196391}i}{2\times 3782}$$

2 ni 3782 marotabaga ko'paytirish.

$$x=\frac{-165735±5\sqrt{53967196391}i}{7564}$$

x=\frac{-165735±5\sqrt{53967196391}i}{7564} tenglamasini yeching, bunda ± musbat. -165735 ni 5i\sqrt{53967196391} ga qo'shish.

$$x=\frac{-165735+5\sqrt{53967196391}i}{7564}$$

x=\frac{-165735±5\sqrt{53967196391}i}{7564} tenglamasini yeching, bunda ± manfiy. -165735 dan 5i\sqrt{53967196391} ni ayirish.

$$x=\frac{-5\sqrt{53967196391}i-165735}{7564}$$

Tenglama yechildi.

$$x=\frac{-165735+5\sqrt{53967196391}i}{7564} x=\frac{-5\sqrt{53967196391}i-165735}{7564}$$

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.

$$3782x^{2}+165735x+91000000=0$$

Tenglamaning ikkala tarafidan 91000000 ni ayirish.

$$3782x^{2}+165735x+91000000-91000000=-91000000$$

O‘zidan 91000000 ayirilsa 0 qoladi.

$$3782x^{2}+165735x=-91000000$$

Ikki tarafini 3782 ga bo‘ling.

$$\frac{3782x^{2}+165735x}{3782}=-\frac{91000000}{3782}$$

3782 ga bo'lish 3782 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{165735}{3782}x=-\frac{91000000}{3782}$$

\frac{-91000000}{3782} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}+\frac{165735}{3782}x=-\frac{45500000}{1891}$$

\frac{165735}{3782} ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{165735}{7564} olish uchun. Keyin, \frac{165735}{7564} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+\frac{165735}{3782}x+\left(\frac{165735}{7564}\right)^{2}=-\frac{45500000}{1891}+\left(\frac{165735}{7564}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{165735}{7564} kvadratini chiqarish.

$$x^{2}+\frac{165735}{3782}x+\frac{27468090225}{57214096}=-\frac{45500000}{1891}+\frac{27468090225}{57214096}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali -\frac{45500000}{1891} ni \frac{27468090225}{57214096} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}+\frac{165735}{3782}x+\frac{27468090225}{57214096}=-\frac{1349179909775}{57214096}$$

x^{2}+\frac{165735}{3782}x+\frac{27468090225}{57214096} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+\frac{165735}{7564}\right)^{2}=-\frac{1349179909775}{57214096}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{165735}{7564}\right)^{2}}=\sqrt{-\frac{1349179909775}{57214096}}$$

Qisqartirish.

$$x+\frac{165735}{7564}=\frac{5\sqrt{53967196391}i}{7564} x+\frac{165735}{7564}=-\frac{5\sqrt{53967196391}i}{7564}$$

Tenglamaning ikkala tarafidan \frac{165735}{7564} ni ayirish.

$$x=\frac{-165735+5\sqrt{53967196391}i}{7564} x=\frac{-5\sqrt{53967196391}i-165735}{7564}$$