32000000-74640x+3122x^2-0003321x^3=0 eching

$$32000000-74640x+3122 { x }^{ 2 } -0003321 { x }^{ 3 } =0$$

x uchun yechish (complex solution)

$$x=\frac{18660+20\sqrt{61569511}i}{1561}\approx 11,953875721+100,533301455i$$

$$x=\frac{-20\sqrt{61569511}i+18660}{1561}\approx 11,953875721-100,533301455i$$

Kvadrat tenglamalaridan foydalanish qoidalari

0 hosil qilish uchun 0 va 0 ni ko'paytirish.

$$32000000-74640x+3122x^{2}-0\times 0\times 3321x^{3}=0$$

0 hosil qilish uchun 0 va 0 ni ko'paytirish.

$$32000000-74640x+3122x^{2}-0\times 3321x^{3}=0$$

0 hosil qilish uchun 0 va 3321 ni ko'paytirish.

$$32000000-74640x+3122x^{2}-0x^{3}=0$$

Har qanday sonni nolga ko‘paytirsangiz, nol chiqadi.

$$32000000-74640x+3122x^{2}-0=0$$

Shartlarni qayta saralash.

$$3122x^{2}-74640x+32000000=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 3122 ni a, -74640 ni b va 32000000 ni c bilan almashtiring.

$$x=\frac{-\left(-74640\right)±\sqrt{\left(-74640\right)^{2}-4\times 3122\times 32000000}}{2\times 3122}$$

-74640 kvadratini chiqarish.

$$x=\frac{-\left(-74640\right)±\sqrt{5571129600-4\times 3122\times 32000000}}{2\times 3122}$$

-4 ni 3122 marotabaga ko'paytirish.

$$x=\frac{-\left(-74640\right)±\sqrt{5571129600-12488\times 32000000}}{2\times 3122}$$

-12488 ni 32000000 marotabaga ko'paytirish.

$$x=\frac{-\left(-74640\right)±\sqrt{5571129600-399616000000}}{2\times 3122}$$

5571129600 ni -399616000000 ga qo'shish.

$$x=\frac{-\left(-74640\right)±\sqrt{-394044870400}}{2\times 3122}$$

-394044870400 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-74640\right)±80\sqrt{61569511}i}{2\times 3122}$$

-74640 ning teskarisi 74640 ga teng.

$$x=\frac{74640±80\sqrt{61569511}i}{2\times 3122}$$

2 ni 3122 marotabaga ko'paytirish.

$$x=\frac{74640±80\sqrt{61569511}i}{6244}$$

x=\frac{74640±80\sqrt{61569511}i}{6244} tenglamasini yeching, bunda ± musbat. 74640 ni 80i\sqrt{61569511} ga qo'shish.

$$x=\frac{74640+80\sqrt{61569511}i}{6244}$$

74640+80i\sqrt{61569511} ni 6244 ga bo'lish.

$$x=\frac{18660+20\sqrt{61569511}i}{1561}$$

x=\frac{74640±80\sqrt{61569511}i}{6244} tenglamasini yeching, bunda ± manfiy. 74640 dan 80i\sqrt{61569511} ni ayirish.

$$x=\frac{-80\sqrt{61569511}i+74640}{6244}$$

74640-80i\sqrt{61569511} ni 6244 ga bo'lish.

$$x=\frac{-20\sqrt{61569511}i+18660}{1561}$$

Tenglama yechildi.

$$x=\frac{18660+20\sqrt{61569511}i}{1561} x=\frac{-20\sqrt{61569511}i+18660}{1561}$$

Kvadratni yakunlash bo'yicha qadamlar

0 hosil qilish uchun 0 va 0 ni ko'paytirish.

$$32000000-74640x+3122x^{2}-0\times 0\times 3321x^{3}=0$$

0 hosil qilish uchun 0 va 0 ni ko'paytirish.

$$32000000-74640x+3122x^{2}-0\times 3321x^{3}=0$$

0 hosil qilish uchun 0 va 3321 ni ko'paytirish.

$$32000000-74640x+3122x^{2}-0x^{3}=0$$

Har qanday sonni nolga ko‘paytirsangiz, nol chiqadi.

$$32000000-74640x+3122x^{2}-0=0$$

0 ni ikki tarafga qo’shing.

$$32000000-74640x+3122x^{2}=0+0$$

0 olish uchun 0 va 0'ni qo'shing.

$$32000000-74640x+3122x^{2}=0$$

Ikkala tarafdan 32000000 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$-74640x+3122x^{2}=-32000000$$

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

$$3122x^{2}-74640x=-32000000$$

Ikki tarafini 3122 ga bo‘ling.

$$\frac{3122x^{2}-74640x}{3122}=-\frac{32000000}{3122}$$

3122 ga bo'lish 3122 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{74640}{3122}\right)x=-\frac{32000000}{3122}$$

\frac{-74640}{3122} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}-\frac{37320}{1561}x=-\frac{32000000}{3122}$$

\frac{-32000000}{3122} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}-\frac{37320}{1561}x=-\frac{16000000}{1561}$$

-\frac{37320}{1561} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{18660}{1561} olish uchun. Keyin, -\frac{18660}{1561} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{37320}{1561}x+\left(-\frac{18660}{1561}\right)^{2}=-\frac{16000000}{1561}+\left(-\frac{18660}{1561}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{18660}{1561} kvadratini chiqarish.

$$x^{2}-\frac{37320}{1561}x+\frac{348195600}{2436721}=-\frac{16000000}{1561}+\frac{348195600}{2436721}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali -\frac{16000000}{1561} ni \frac{348195600}{2436721} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}-\frac{37320}{1561}x+\frac{348195600}{2436721}=-\frac{24627804400}{2436721}$$

x^{2}-\frac{37320}{1561}x+\frac{348195600}{2436721} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{18660}{1561}\right)^{2}=-\frac{24627804400}{2436721}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{18660}{1561}\right)^{2}}=\sqrt{-\frac{24627804400}{2436721}}$$

Qisqartirish.

$$x-\frac{18660}{1561}=\frac{20\sqrt{61569511}i}{1561} x-\frac{18660}{1561}=-\frac{20\sqrt{61569511}i}{1561}$$

\frac{18660}{1561} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{18660+20\sqrt{61569511}i}{1561} x=\frac{-20\sqrt{61569511}i+18660}{1561}$$