1064=4+6(x-1)/2*x eching

$$1064 = \frac { 4 + 6 ( x - 1 ) } { 2 } \cdot x$$

x uchun yechish

$$x = -\frac{56}{3} = -18\frac{2}{3} \approx -18,666666667$$

$$x=19$$

Kvadrat tenglamalaridan foydalanish qoidalari

Tenglamaning ikkala tarafini 2 ga ko'paytirish.

$$2128=\left(4+6\left(x-1\right)\right)x$$

6 ga x-1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$2128=\left(4+6x-6\right)x$$

-2 olish uchun 4 dan 6 ni ayirish.

$$2128=\left(-2+6x\right)x$$

-2+6x ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$2128=-2x+6x^{2}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$-2x+6x^{2}=2128$$

Ikkala tarafdan 2128 ni ayirish.

$$-2x+6x^{2}-2128=0$$

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.

$$6x^{2}-2x-2128=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 6 ni a, -2 ni b va -2128 ni c bilan almashtiring.

$$x=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\times 6\left(-2128\right)}}{2\times 6}$$

-2 kvadratini chiqarish.

$$x=\frac{-\left(-2\right)±\sqrt{4-4\times 6\left(-2128\right)}}{2\times 6}$$

-4 ni 6 marotabaga ko'paytirish.

$$x=\frac{-\left(-2\right)±\sqrt{4-24\left(-2128\right)}}{2\times 6}$$

-24 ni -2128 marotabaga ko'paytirish.

$$x=\frac{-\left(-2\right)±\sqrt{4+51072}}{2\times 6}$$

4 ni 51072 ga qo'shish.

$$x=\frac{-\left(-2\right)±\sqrt{51076}}{2\times 6}$$

51076 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-2\right)±226}{2\times 6}$$

-2 ning teskarisi 2 ga teng.

$$x=\frac{2±226}{2\times 6}$$

2 ni 6 marotabaga ko'paytirish.

$$x=\frac{2±226}{12}$$

x=\frac{2±226}{12} tenglamasini yeching, bunda ± musbat. 2 ni 226 ga qo'shish.

$$x=\frac{228}{12}$$

228 ni 12 ga bo'lish.

$$x=19$$

x=\frac{2±226}{12} tenglamasini yeching, bunda ± manfiy. 2 dan 226 ni ayirish.

$$x=-\frac{224}{12}$$

\frac{-224}{12} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=-\frac{56}{3}$$

Tenglama yechildi.

$$x=19 x=-\frac{56}{3}$$

Kvadratni yakunlash bo'yicha qadamlar

Tenglamaning ikkala tarafini 2 ga ko'paytirish.

$$2128=\left(4+6\left(x-1\right)\right)x$$

6 ga x-1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$2128=\left(4+6x-6\right)x$$

-2 olish uchun 4 dan 6 ni ayirish.

$$2128=\left(-2+6x\right)x$$

-2+6x ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$2128=-2x+6x^{2}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$-2x+6x^{2}=2128$$

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

$$6x^{2}-2x=2128$$

Ikki tarafini 6 ga bo‘ling.

$$\frac{6x^{2}-2x}{6}=\frac{2128}{6}$$

6 ga bo'lish 6 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{2}{6}\right)x=\frac{2128}{6}$$

\frac{-2}{6} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}-\frac{1}{3}x=\frac{2128}{6}$$

\frac{2128}{6} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}-\frac{1}{3}x=\frac{1064}{3}$$

-\frac{1}{3} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{1}{6} olish uchun. Keyin, -\frac{1}{6} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{1}{3}x+\left(-\frac{1}{6}\right)^{2}=\frac{1064}{3}+\left(-\frac{1}{6}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{1}{6} kvadratini chiqarish.

$$x^{2}-\frac{1}{3}x+\frac{1}{36}=\frac{1064}{3}+\frac{1}{36}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{1064}{3} ni \frac{1}{36} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}-\frac{1}{3}x+\frac{1}{36}=\frac{12769}{36}$$

x^{2}-\frac{1}{3}x+\frac{1}{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.

$$\left(x-\frac{1}{6}\right)^{2}=\frac{12769}{36}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{1}{6}\right)^{2}}=\sqrt{\frac{12769}{36}}$$

Qisqartirish.

$$x-\frac{1}{6}=\frac{113}{6} x-\frac{1}{6}=-\frac{113}{6}$$

\frac{1}{6} ni tenglamaning ikkala tarafiga qo'shish.

$$x=19 x=-\frac{56}{3}$$