21x^2-6x=13 eching

$$21 x ^ { 2 } - 6 x = 13$$

x uchun yechish

$$x=\frac{\sqrt{282}}{21}+\frac{1}{7}\approx 0,942516934$$

$$x=-\frac{\sqrt{282}}{21}+\frac{1}{7}\approx -0,656802649$$

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.

$$21x^{2}-6x=13$$

Tenglamaning ikkala tarafidan 13 ni ayirish.

$$21x^{2}-6x-13=13-13$$

O‘zidan 13 ayirilsa 0 qoladi.

$$21x^{2}-6x-13=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 21 ni a, -6 ni b va -13 ni c bilan almashtiring.

$$x=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}-4\times 21\left(-13\right)}}{2\times 21}$$

-6 kvadratini chiqarish.

$$x=\frac{-\left(-6\right)±\sqrt{36-4\times 21\left(-13\right)}}{2\times 21}$$

-4 ni 21 marotabaga ko'paytirish.

$$x=\frac{-\left(-6\right)±\sqrt{36-84\left(-13\right)}}{2\times 21}$$

-84 ni -13 marotabaga ko'paytirish.

$$x=\frac{-\left(-6\right)±\sqrt{36+1092}}{2\times 21}$$

36 ni 1092 ga qo'shish.

$$x=\frac{-\left(-6\right)±\sqrt{1128}}{2\times 21}$$

1128 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-6\right)±2\sqrt{282}}{2\times 21}$$

-6 ning teskarisi 6 ga teng.

$$x=\frac{6±2\sqrt{282}}{2\times 21}$$

2 ni 21 marotabaga ko'paytirish.

$$x=\frac{6±2\sqrt{282}}{42}$$

x=\frac{6±2\sqrt{282}}{42} tenglamasini yeching, bunda ± musbat. 6 ni 2\sqrt{282} ga qo'shish.

$$x=\frac{2\sqrt{282}+6}{42}$$

6+2\sqrt{282} ni 42 ga bo'lish.

$$x=\frac{\sqrt{282}}{21}+\frac{1}{7}$$

x=\frac{6±2\sqrt{282}}{42} tenglamasini yeching, bunda ± manfiy. 6 dan 2\sqrt{282} ni ayirish.

$$x=\frac{6-2\sqrt{282}}{42}$$

6-2\sqrt{282} ni 42 ga bo'lish.

$$x=-\frac{\sqrt{282}}{21}+\frac{1}{7}$$

Tenglama yechildi.

$$x=\frac{\sqrt{282}}{21}+\frac{1}{7} x=-\frac{\sqrt{282}}{21}+\frac{1}{7}$$

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.

$$21x^{2}-6x=13$$

Ikki tarafini 21 ga bo‘ling.

$$\frac{21x^{2}-6x}{21}=\frac{13}{21}$$

21 ga bo'lish 21 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{6}{21}\right)x=\frac{13}{21}$$

\frac{-6}{21} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}-\frac{2}{7}x=\frac{13}{21}$$

-\frac{2}{7} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{1}{7} olish uchun. Keyin, -\frac{1}{7} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{2}{7}x+\left(-\frac{1}{7}\right)^{2}=\frac{13}{21}+\left(-\frac{1}{7}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{1}{7} kvadratini chiqarish.

$$x^{2}-\frac{2}{7}x+\frac{1}{49}=\frac{13}{21}+\frac{1}{49}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{13}{21} ni \frac{1}{49} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}-\frac{2}{7}x+\frac{1}{49}=\frac{94}{147}$$

x^{2}-\frac{2}{7}x+\frac{1}{49} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{1}{7}\right)^{2}=\frac{94}{147}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{1}{7}\right)^{2}}=\sqrt{\frac{94}{147}}$$

Qisqartirish.

$$x-\frac{1}{7}=\frac{\sqrt{282}}{21} x-\frac{1}{7}=-\frac{\sqrt{282}}{21}$$

\frac{1}{7} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{\sqrt{282}}{21}+\frac{1}{7} x=-\frac{\sqrt{282}}{21}+\frac{1}{7}$$