x^2*10div6+6=765-2x eching

$${ x }^{ 2 } \times 10 \div 6+6=765-2x$$

x uchun yechish

$$x = \frac{3 \sqrt{1266} - 3}{5} \approx 20,74853625$$

$$x=\frac{-3\sqrt{1266}-3}{5}\approx -21,94853625$$

Kvadrat tenglamalaridan foydalanish qoidalari

Tenglamaning ikkala tarafini 6 ga ko'paytirish.

$$x^{2}\times 10+36=4590-12x$$

Ikkala tarafdan 4590 ni ayirish.

$$x^{2}\times 10+36-4590=-12x$$

-4554 olish uchun 36 dan 4590 ni ayirish.

$$x^{2}\times 10-4554=-12x$$

12x ni ikki tarafga qo’shing.

$$x^{2}\times 10-4554+12x=0$$

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.

$$10x^{2}+12x-4554=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 10 ni a, 12 ni b va -4554 ni c bilan almashtiring.

$$x=\frac{-12±\sqrt{12^{2}-4\times 10\left(-4554\right)}}{2\times 10}$$

12 kvadratini chiqarish.

$$x=\frac{-12±\sqrt{144-4\times 10\left(-4554\right)}}{2\times 10}$$

-4 ni 10 marotabaga ko'paytirish.

$$x=\frac{-12±\sqrt{144-40\left(-4554\right)}}{2\times 10}$$

-40 ni -4554 marotabaga ko'paytirish.

$$x=\frac{-12±\sqrt{144+182160}}{2\times 10}$$

144 ni 182160 ga qo'shish.

$$x=\frac{-12±\sqrt{182304}}{2\times 10}$$

182304 ning kvadrat ildizini chiqarish.

$$x=\frac{-12±12\sqrt{1266}}{2\times 10}$$

2 ni 10 marotabaga ko'paytirish.

$$x=\frac{-12±12\sqrt{1266}}{20}$$

x=\frac{-12±12\sqrt{1266}}{20} tenglamasini yeching, bunda ± musbat. -12 ni 12\sqrt{1266} ga qo'shish.

$$x=\frac{12\sqrt{1266}-12}{20}$$

-12+12\sqrt{1266} ni 20 ga bo'lish.

$$x=\frac{3\sqrt{1266}-3}{5}$$

x=\frac{-12±12\sqrt{1266}}{20} tenglamasini yeching, bunda ± manfiy. -12 dan 12\sqrt{1266} ni ayirish.

$$x=\frac{-12\sqrt{1266}-12}{20}$$

-12-12\sqrt{1266} ni 20 ga bo'lish.

$$x=\frac{-3\sqrt{1266}-3}{5}$$

Tenglama yechildi.

$$x=\frac{3\sqrt{1266}-3}{5} x=\frac{-3\sqrt{1266}-3}{5}$$

Kvadratni yakunlash bo'yicha qadamlar

Tenglamaning ikkala tarafini 6 ga ko'paytirish.

$$x^{2}\times 10+36=4590-12x$$

12x ni ikki tarafga qo’shing.

$$x^{2}\times 10+36+12x=4590$$

Ikkala tarafdan 36 ni ayirish.

$$x^{2}\times 10+12x=4590-36$$

4554 olish uchun 4590 dan 36 ni ayirish.

$$x^{2}\times 10+12x=4554$$

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

$$10x^{2}+12x=4554$$

Ikki tarafini 10 ga bo‘ling.

$$\frac{10x^{2}+12x}{10}=\frac{4554}{10}$$

10 ga bo'lish 10 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{12}{10}x=\frac{4554}{10}$$

\frac{12}{10} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}+\frac{6}{5}x=\frac{4554}{10}$$

\frac{4554}{10} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}+\frac{6}{5}x=\frac{2277}{5}$$

\frac{6}{5} ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{3}{5} olish uchun. Keyin, \frac{3}{5} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+\frac{6}{5}x+\left(\frac{3}{5}\right)^{2}=\frac{2277}{5}+\left(\frac{3}{5}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{3}{5} kvadratini chiqarish.

$$x^{2}+\frac{6}{5}x+\frac{9}{25}=\frac{2277}{5}+\frac{9}{25}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{2277}{5} ni \frac{9}{25} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}+\frac{6}{5}x+\frac{9}{25}=\frac{11394}{25}$$

x^{2}+\frac{6}{5}x+\frac{9}{25} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+\frac{3}{5}\right)^{2}=\frac{11394}{25}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{3}{5}\right)^{2}}=\sqrt{\frac{11394}{25}}$$

Qisqartirish.

$$x+\frac{3}{5}=\frac{3\sqrt{1266}}{5} x+\frac{3}{5}=-\frac{3\sqrt{1266}}{5}$$

Tenglamaning ikkala tarafidan \frac{3}{5} ni ayirish.

$$x=\frac{3\sqrt{1266}-3}{5} x=\frac{-3\sqrt{1266}-3}{5}$$