32/3x1/6-3/4left(2x+18right)=-4 eching

$$3 \frac{ 2 }{ 3x } \frac{ 1 }{ 6 } - \frac{ 3 }{ 4 } \left( 2x+18 \right) = -4$$

x uchun yechish

$$x=\frac{\sqrt{41}}{2}-\frac{19}{6}\approx 0,034895452$$

$$x=-\frac{\sqrt{41}}{2}-\frac{19}{6}\approx -6,368228785$$

Kvadrat tenglamalaridan foydalanish qoidalari

x qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 12x ga, 3x,6,4 ning eng kichik karralisiga ko‘paytiring.

$$3\times 4\times 2\times \frac{1}{6}-\frac{3}{4}\left(2x+18\right)\times 12x=-48x$$

12 hosil qilish uchun 3 va 4 ni ko'paytirish.

$$12\times 2\times \frac{1}{6}-\frac{3}{4}\left(2x+18\right)\times 12x=-48x$$

24 hosil qilish uchun 12 va 2 ni ko'paytirish.

$$24\times \frac{1}{6}-\frac{3}{4}\left(2x+18\right)\times 12x=-48x$$

4 hosil qilish uchun 24 va \frac{1}{6} ni ko'paytirish.

$$4-\frac{3}{4}\left(2x+18\right)\times 12x=-48x$$

-9 hosil qilish uchun -\frac{3}{4} va 12 ni ko'paytirish.

$$4-9\left(2x+18\right)x=-48x$$

-9 ga 2x+18 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$4+\left(-18x-162\right)x=-48x$$

-18x-162 ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$4-18x^{2}-162x=-48x$$

48x ni ikki tarafga qo’shing.

$$4-18x^{2}-162x+48x=0$$

-114x ni olish uchun -162x va 48x ni birlashtirish.

$$4-18x^{2}-114x=0$$

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.

$$-18x^{2}-114x+4=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -18 ni a, -114 ni b va 4 ni c bilan almashtiring.

$$x=\frac{-\left(-114\right)±\sqrt{\left(-114\right)^{2}-4\left(-18\right)\times 4}}{2\left(-18\right)}$$

-114 kvadratini chiqarish.

$$x=\frac{-\left(-114\right)±\sqrt{12996-4\left(-18\right)\times 4}}{2\left(-18\right)}$$

-4 ni -18 marotabaga ko'paytirish.

$$x=\frac{-\left(-114\right)±\sqrt{12996+72\times 4}}{2\left(-18\right)}$$

72 ni 4 marotabaga ko'paytirish.

$$x=\frac{-\left(-114\right)±\sqrt{12996+288}}{2\left(-18\right)}$$

12996 ni 288 ga qo'shish.

$$x=\frac{-\left(-114\right)±\sqrt{13284}}{2\left(-18\right)}$$

13284 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-114\right)±18\sqrt{41}}{2\left(-18\right)}$$

-114 ning teskarisi 114 ga teng.

$$x=\frac{114±18\sqrt{41}}{2\left(-18\right)}$$

2 ni -18 marotabaga ko'paytirish.

$$x=\frac{114±18\sqrt{41}}{-36}$$

x=\frac{114±18\sqrt{41}}{-36} tenglamasini yeching, bunda ± musbat. 114 ni 18\sqrt{41} ga qo'shish.

$$x=\frac{18\sqrt{41}+114}{-36}$$

114+18\sqrt{41} ni -36 ga bo'lish.

$$x=-\frac{\sqrt{41}}{2}-\frac{19}{6}$$

x=\frac{114±18\sqrt{41}}{-36} tenglamasini yeching, bunda ± manfiy. 114 dan 18\sqrt{41} ni ayirish.

$$x=\frac{114-18\sqrt{41}}{-36}$$

114-18\sqrt{41} ni -36 ga bo'lish.

$$x=\frac{\sqrt{41}}{2}-\frac{19}{6}$$

Tenglama yechildi.

$$x=-\frac{\sqrt{41}}{2}-\frac{19}{6} x=\frac{\sqrt{41}}{2}-\frac{19}{6}$$

Kvadratni yakunlash bo'yicha qadamlar

x qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 12x ga, 3x,6,4 ning eng kichik karralisiga ko‘paytiring.

$$3\times 4\times 2\times \frac{1}{6}-\frac{3}{4}\left(2x+18\right)\times 12x=-48x$$

12 hosil qilish uchun 3 va 4 ni ko'paytirish.

$$12\times 2\times \frac{1}{6}-\frac{3}{4}\left(2x+18\right)\times 12x=-48x$$

24 hosil qilish uchun 12 va 2 ni ko'paytirish.

$$24\times \frac{1}{6}-\frac{3}{4}\left(2x+18\right)\times 12x=-48x$$

4 hosil qilish uchun 24 va \frac{1}{6} ni ko'paytirish.

$$4-\frac{3}{4}\left(2x+18\right)\times 12x=-48x$$

-9 hosil qilish uchun -\frac{3}{4} va 12 ni ko'paytirish.

$$4-9\left(2x+18\right)x=-48x$$

-9 ga 2x+18 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$4+\left(-18x-162\right)x=-48x$$

-18x-162 ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$4-18x^{2}-162x=-48x$$

48x ni ikki tarafga qo’shing.

$$4-18x^{2}-162x+48x=0$$

-114x ni olish uchun -162x va 48x ni birlashtirish.

$$4-18x^{2}-114x=0$$

Ikkala tarafdan 4 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$-18x^{2}-114x=-4$$

Ikki tarafini -18 ga bo‘ling.

$$\frac{-18x^{2}-114x}{-18}=-\frac{4}{-18}$$

-18 ga bo'lish -18 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{114}{-18}\right)x=-\frac{4}{-18}$$

\frac{-114}{-18} ulushini 6 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}+\frac{19}{3}x=-\frac{4}{-18}$$

\frac{-4}{-18} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}+\frac{19}{3}x=\frac{2}{9}$$

\frac{19}{3} ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{19}{6} olish uchun. Keyin, \frac{19}{6} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+\frac{19}{3}x+\left(\frac{19}{6}\right)^{2}=\frac{2}{9}+\left(\frac{19}{6}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{19}{6} kvadratini chiqarish.

$$x^{2}+\frac{19}{3}x+\frac{361}{36}=\frac{2}{9}+\frac{361}{36}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{2}{9} ni \frac{361}{36} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}+\frac{19}{3}x+\frac{361}{36}=\frac{41}{4}$$

x^{2}+\frac{19}{3}x+\frac{361}{36} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+\frac{19}{6}\right)^{2}=\frac{41}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{19}{6}\right)^{2}}=\sqrt{\frac{41}{4}}$$

Qisqartirish.

$$x+\frac{19}{6}=\frac{\sqrt{41}}{2} x+\frac{19}{6}=-\frac{\sqrt{41}}{2}$$

Tenglamaning ikkala tarafidan \frac{19}{6} ni ayirish.

$$x=\frac{\sqrt{41}}{2}-\frac{19}{6} x=-\frac{\sqrt{41}}{2}-\frac{19}{6}$$