26x(2x-6/3=32x+1x^2-6 eching

$$\frac { 26 x ( 2 x - 6 } { 3 } = 32 x + 1 x ^ { 2 } - 6$$

x uchun yechish

$$x = \frac{3 \sqrt{34} + 18}{7} \approx 5,070407955$$

$$x=\frac{18-3\sqrt{34}}{7}\approx 0,072449188$$

Kvadrat tenglamalaridan foydalanish qoidalari

Tenglamaning ikkala tarafini 3 ga ko'paytirish.

$$26x\left(2x-6\right)=96x+3x^{2}-18$$

26x ga 2x-6 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$52x^{2}-156x=96x+3x^{2}-18$$

Ikkala tarafdan 96x ni ayirish.

$$52x^{2}-156x-96x=3x^{2}-18$$

-252x ni olish uchun -156x va -96x ni birlashtirish.

$$52x^{2}-252x=3x^{2}-18$$

Ikkala tarafdan 3x^{2} ni ayirish.

$$52x^{2}-252x-3x^{2}=-18$$

49x^{2} ni olish uchun 52x^{2} va -3x^{2} ni birlashtirish.

$$49x^{2}-252x=-18$$

18 ni ikki tarafga qo’shing.

$$49x^{2}-252x+18=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 49 ni a, -252 ni b va 18 ni c bilan almashtiring.

$$x=\frac{-\left(-252\right)±\sqrt{\left(-252\right)^{2}-4\times 49\times 18}}{2\times 49}$$

-252 kvadratini chiqarish.

$$x=\frac{-\left(-252\right)±\sqrt{63504-4\times 49\times 18}}{2\times 49}$$

-4 ni 49 marotabaga ko'paytirish.

$$x=\frac{-\left(-252\right)±\sqrt{63504-196\times 18}}{2\times 49}$$

-196 ni 18 marotabaga ko'paytirish.

$$x=\frac{-\left(-252\right)±\sqrt{63504-3528}}{2\times 49}$$

63504 ni -3528 ga qo'shish.

$$x=\frac{-\left(-252\right)±\sqrt{59976}}{2\times 49}$$

59976 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-252\right)±42\sqrt{34}}{2\times 49}$$

-252 ning teskarisi 252 ga teng.

$$x=\frac{252±42\sqrt{34}}{2\times 49}$$

2 ni 49 marotabaga ko'paytirish.

$$x=\frac{252±42\sqrt{34}}{98}$$

x=\frac{252±42\sqrt{34}}{98} tenglamasini yeching, bunda ± musbat. 252 ni 42\sqrt{34} ga qo'shish.

$$x=\frac{42\sqrt{34}+252}{98}$$

252+42\sqrt{34} ni 98 ga bo'lish.

$$x=\frac{3\sqrt{34}+18}{7}$$

x=\frac{252±42\sqrt{34}}{98} tenglamasini yeching, bunda ± manfiy. 252 dan 42\sqrt{34} ni ayirish.

$$x=\frac{252-42\sqrt{34}}{98}$$

252-42\sqrt{34} ni 98 ga bo'lish.

$$x=\frac{18-3\sqrt{34}}{7}$$

Tenglama yechildi.

$$x=\frac{3\sqrt{34}+18}{7} x=\frac{18-3\sqrt{34}}{7}$$

Kvadratni yakunlash bo'yicha qadamlar

Tenglamaning ikkala tarafini 3 ga ko'paytirish.

$$26x\left(2x-6\right)=96x+3x^{2}-18$$

26x ga 2x-6 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$52x^{2}-156x=96x+3x^{2}-18$$

Ikkala tarafdan 96x ni ayirish.

$$52x^{2}-156x-96x=3x^{2}-18$$

-252x ni olish uchun -156x va -96x ni birlashtirish.

$$52x^{2}-252x=3x^{2}-18$$

Ikkala tarafdan 3x^{2} ni ayirish.

$$52x^{2}-252x-3x^{2}=-18$$

49x^{2} ni olish uchun 52x^{2} va -3x^{2} ni birlashtirish.

$$49x^{2}-252x=-18$$

Ikki tarafini 49 ga bo‘ling.

$$\frac{49x^{2}-252x}{49}=-\frac{18}{49}$$

49 ga bo'lish 49 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{252}{49}\right)x=-\frac{18}{49}$$

\frac{-252}{49} ulushini 7 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}-\frac{36}{7}x=-\frac{18}{49}$$

-\frac{36}{7} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{18}{7} olish uchun. Keyin, -\frac{18}{7} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{36}{7}x+\left(-\frac{18}{7}\right)^{2}=-\frac{18}{49}+\left(-\frac{18}{7}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{18}{7} kvadratini chiqarish.

$$x^{2}-\frac{36}{7}x+\frac{324}{49}=\frac{-18+324}{49}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali -\frac{18}{49} ni \frac{324}{49} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}-\frac{36}{7}x+\frac{324}{49}=\frac{306}{49}$$

x^{2}-\frac{36}{7}x+\frac{324}{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.

$$\left(x-\frac{18}{7}\right)^{2}=\frac{306}{49}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{18}{7}\right)^{2}}=\sqrt{\frac{306}{49}}$$

Qisqartirish.

$$x-\frac{18}{7}=\frac{3\sqrt{34}}{7} x-\frac{18}{7}=-\frac{3\sqrt{34}}{7}$$

\frac{18}{7} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{3\sqrt{34}+18}{7} x=\frac{18-3\sqrt{34}}{7}$$