365x^2-7317x+365000=0 eching

$$365 x ^ { 2 } - 7317 x + 365000 = 0$$

x uchun yechish (complex solution)

$$x=\frac{7317+\sqrt{479361511}i}{730}\approx 10,023287671+29,992227397i$$

$$x=\frac{-\sqrt{479361511}i+7317}{730}\approx 10,023287671-29,992227397i$$

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.

$$365x^{2}-7317x+365000=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 365 ni a, -7317 ni b va 365000 ni c bilan almashtiring.

$$x=\frac{-\left(-7317\right)±\sqrt{\left(-7317\right)^{2}-4\times 365\times 365000}}{2\times 365}$$

-7317 kvadratini chiqarish.

$$x=\frac{-\left(-7317\right)±\sqrt{53538489-4\times 365\times 365000}}{2\times 365}$$

-4 ni 365 marotabaga ko'paytirish.

$$x=\frac{-\left(-7317\right)±\sqrt{53538489-1460\times 365000}}{2\times 365}$$

-1460 ni 365000 marotabaga ko'paytirish.

$$x=\frac{-\left(-7317\right)±\sqrt{53538489-532900000}}{2\times 365}$$

53538489 ni -532900000 ga qo'shish.

$$x=\frac{-\left(-7317\right)±\sqrt{-479361511}}{2\times 365}$$

-479361511 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-7317\right)±\sqrt{479361511}i}{2\times 365}$$

-7317 ning teskarisi 7317 ga teng.

$$x=\frac{7317±\sqrt{479361511}i}{2\times 365}$$

2 ni 365 marotabaga ko'paytirish.

$$x=\frac{7317±\sqrt{479361511}i}{730}$$

x=\frac{7317±\sqrt{479361511}i}{730} tenglamasini yeching, bunda ± musbat. 7317 ni i\sqrt{479361511} ga qo'shish.

$$x=\frac{7317+\sqrt{479361511}i}{730}$$

x=\frac{7317±\sqrt{479361511}i}{730} tenglamasini yeching, bunda ± manfiy. 7317 dan i\sqrt{479361511} ni ayirish.

$$x=\frac{-\sqrt{479361511}i+7317}{730}$$

Tenglama yechildi.

$$x=\frac{7317+\sqrt{479361511}i}{730} x=\frac{-\sqrt{479361511}i+7317}{730}$$

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.

$$365x^{2}-7317x+365000=0$$

Tenglamaning ikkala tarafidan 365000 ni ayirish.

$$365x^{2}-7317x+365000-365000=-365000$$

O‘zidan 365000 ayirilsa 0 qoladi.

$$365x^{2}-7317x=-365000$$

Ikki tarafini 365 ga bo‘ling.

$$\frac{365x^{2}-7317x}{365}=-\frac{365000}{365}$$

365 ga bo'lish 365 ga ko'paytirishni bekor qiladi.

$$x^{2}-\frac{7317}{365}x=-\frac{365000}{365}$$

-365000 ni 365 ga bo'lish.

$$x^{2}-\frac{7317}{365}x=-1000$$

-\frac{7317}{365} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{7317}{730} olish uchun. Keyin, -\frac{7317}{730} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{7317}{365}x+\left(-\frac{7317}{730}\right)^{2}=-1000+\left(-\frac{7317}{730}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{7317}{730} kvadratini chiqarish.

$$x^{2}-\frac{7317}{365}x+\frac{53538489}{532900}=-1000+\frac{53538489}{532900}$$

-1000 ni \frac{53538489}{532900} ga qo'shish.

$$x^{2}-\frac{7317}{365}x+\frac{53538489}{532900}=-\frac{479361511}{532900}$$

x^{2}-\frac{7317}{365}x+\frac{53538489}{532900} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{7317}{730}\right)^{2}=-\frac{479361511}{532900}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{7317}{730}\right)^{2}}=\sqrt{-\frac{479361511}{532900}}$$

Qisqartirish.

$$x-\frac{7317}{730}=\frac{\sqrt{479361511}i}{730} x-\frac{7317}{730}=-\frac{\sqrt{479361511}i}{730}$$

\frac{7317}{730} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{7317+\sqrt{479361511}i}{730} x=\frac{-\sqrt{479361511}i+7317}{730}$$