13158x^2-2756x+27360=0 eching

$$13158 { x }^{ 2 } -2756x+27360=0$$

x uchun yechish (complex solution)

$$x=\frac{689+\sqrt{89525999}i}{6579}\approx 0,104727162+1,438184824i$$

$$x=\frac{-\sqrt{89525999}i+689}{6579}\approx 0,104727162-1,438184824i$$

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.

$$13158x^{2}-2756x+27360=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 13158 ni a, -2756 ni b va 27360 ni c bilan almashtiring.

$$x=\frac{-\left(-2756\right)±\sqrt{\left(-2756\right)^{2}-4\times 13158\times 27360}}{2\times 13158}$$

-2756 kvadratini chiqarish.

$$x=\frac{-\left(-2756\right)±\sqrt{7595536-4\times 13158\times 27360}}{2\times 13158}$$

-4 ni 13158 marotabaga ko'paytirish.

$$x=\frac{-\left(-2756\right)±\sqrt{7595536-52632\times 27360}}{2\times 13158}$$

-52632 ni 27360 marotabaga ko'paytirish.

$$x=\frac{-\left(-2756\right)±\sqrt{7595536-1440011520}}{2\times 13158}$$

7595536 ni -1440011520 ga qo'shish.

$$x=\frac{-\left(-2756\right)±\sqrt{-1432415984}}{2\times 13158}$$

-1432415984 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-2756\right)±4\sqrt{89525999}i}{2\times 13158}$$

-2756 ning teskarisi 2756 ga teng.

$$x=\frac{2756±4\sqrt{89525999}i}{2\times 13158}$$

2 ni 13158 marotabaga ko'paytirish.

$$x=\frac{2756±4\sqrt{89525999}i}{26316}$$

x=\frac{2756±4\sqrt{89525999}i}{26316} tenglamasini yeching, bunda ± musbat. 2756 ni 4i\sqrt{89525999} ga qo'shish.

$$x=\frac{2756+4\sqrt{89525999}i}{26316}$$

2756+4i\sqrt{89525999} ni 26316 ga bo'lish.

$$x=\frac{689+\sqrt{89525999}i}{6579}$$

x=\frac{2756±4\sqrt{89525999}i}{26316} tenglamasini yeching, bunda ± manfiy. 2756 dan 4i\sqrt{89525999} ni ayirish.

$$x=\frac{-4\sqrt{89525999}i+2756}{26316}$$

2756-4i\sqrt{89525999} ni 26316 ga bo'lish.

$$x=\frac{-\sqrt{89525999}i+689}{6579}$$

Tenglama yechildi.

$$x=\frac{689+\sqrt{89525999}i}{6579} x=\frac{-\sqrt{89525999}i+689}{6579}$$

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.

$$13158x^{2}-2756x+27360=0$$

Tenglamaning ikkala tarafidan 27360 ni ayirish.

$$13158x^{2}-2756x+27360-27360=-27360$$

O‘zidan 27360 ayirilsa 0 qoladi.

$$13158x^{2}-2756x=-27360$$

Ikki tarafini 13158 ga bo‘ling.

$$\frac{13158x^{2}-2756x}{13158}=-\frac{27360}{13158}$$

13158 ga bo'lish 13158 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{2756}{13158}\right)x=-\frac{27360}{13158}$$

\frac{-2756}{13158} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}-\frac{1378}{6579}x=-\frac{27360}{13158}$$

\frac{-27360}{13158} ulushini 18 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}-\frac{1378}{6579}x=-\frac{1520}{731}$$

-\frac{1378}{6579} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{689}{6579} olish uchun. Keyin, -\frac{689}{6579} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{1378}{6579}x+\left(-\frac{689}{6579}\right)^{2}=-\frac{1520}{731}+\left(-\frac{689}{6579}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{689}{6579} kvadratini chiqarish.

$$x^{2}-\frac{1378}{6579}x+\frac{474721}{43283241}=-\frac{1520}{731}+\frac{474721}{43283241}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali -\frac{1520}{731} ni \frac{474721}{43283241} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}-\frac{1378}{6579}x+\frac{474721}{43283241}=-\frac{89525999}{43283241}$$

x^{2}-\frac{1378}{6579}x+\frac{474721}{43283241} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{689}{6579}\right)^{2}=-\frac{89525999}{43283241}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{689}{6579}\right)^{2}}=\sqrt{-\frac{89525999}{43283241}}$$

Qisqartirish.

$$x-\frac{689}{6579}=\frac{\sqrt{89525999}i}{6579} x-\frac{689}{6579}=-\frac{\sqrt{89525999}i}{6579}$$

\frac{689}{6579} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{689+\sqrt{89525999}i}{6579} x=\frac{-\sqrt{89525999}i+689}{6579}$$