-5-6/w-7=-7/(w+1)(w-7) eching

$$- 5 - \frac { 6 } { w - 7 } = - \frac { 7 } { ( w + 1 ) ( w - 7 ) }$$

w uchun yechish

$$w = -\frac{6}{5} = -1\frac{1}{5} = -1,2$$

$$w=6$$

Kvadrat tenglamalaridan foydalanish qoidalari

w qiymati -1,7 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini \left(w-7\right)\left(w+1\right) ga, w-7,\left(w+1\right)\left(w-7\right) ning eng kichik karralisiga ko‘paytiring.

$$\left(w-7\right)\left(w+1\right)\left(-5\right)-\left(w+1\right)\times 6=-7$$

w-7 ga w+1 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$\left(w^{2}-6w-7\right)\left(-5\right)-\left(w+1\right)\times 6=-7$$

w^{2}-6w-7 ga -5 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-5w^{2}+30w+35-\left(w+1\right)\times 6=-7$$

w+1 ga 6 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-5w^{2}+30w+35-\left(6w+6\right)=-7$$

6w+6 teskarisini topish uchun har birining teskarisini toping.

$$-5w^{2}+30w+35-6w-6=-7$$

24w ni olish uchun 30w va -6w ni birlashtirish.

$$-5w^{2}+24w+35-6=-7$$

29 olish uchun 35 dan 6 ni ayirish.

$$-5w^{2}+24w+29=-7$$

7 ni ikki tarafga qo’shing.

$$-5w^{2}+24w+29+7=0$$

36 olish uchun 29 va 7'ni qo'shing.

$$-5w^{2}+24w+36=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -5 ni a, 24 ni b va 36 ni c bilan almashtiring.

$$w=\frac{-24±\sqrt{24^{2}-4\left(-5\right)\times 36}}{2\left(-5\right)}$$

24 kvadratini chiqarish.

$$w=\frac{-24±\sqrt{576-4\left(-5\right)\times 36}}{2\left(-5\right)}$$

-4 ni -5 marotabaga ko'paytirish.

$$w=\frac{-24±\sqrt{576+20\times 36}}{2\left(-5\right)}$$

20 ni 36 marotabaga ko'paytirish.

$$w=\frac{-24±\sqrt{576+720}}{2\left(-5\right)}$$

576 ni 720 ga qo'shish.

$$w=\frac{-24±\sqrt{1296}}{2\left(-5\right)}$$

1296 ning kvadrat ildizini chiqarish.

$$w=\frac{-24±36}{2\left(-5\right)}$$

2 ni -5 marotabaga ko'paytirish.

$$w=\frac{-24±36}{-10}$$

w=\frac{-24±36}{-10} tenglamasini yeching, bunda ± musbat. -24 ni 36 ga qo'shish.

$$w=\frac{12}{-10}$$

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

$$w=-\frac{6}{5}$$

w=\frac{-24±36}{-10} tenglamasini yeching, bunda ± manfiy. -24 dan 36 ni ayirish.

$$w=-\frac{60}{-10}$$

-60 ni -10 ga bo'lish.

$$w=6$$

Tenglama yechildi.

$$w=-\frac{6}{5} w=6$$

Kvadratni yakunlash bo'yicha qadamlar

w qiymati -1,7 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini \left(w-7\right)\left(w+1\right) ga, w-7,\left(w+1\right)\left(w-7\right) ning eng kichik karralisiga ko‘paytiring.

$$\left(w-7\right)\left(w+1\right)\left(-5\right)-\left(w+1\right)\times 6=-7$$

w-7 ga w+1 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$\left(w^{2}-6w-7\right)\left(-5\right)-\left(w+1\right)\times 6=-7$$

w^{2}-6w-7 ga -5 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-5w^{2}+30w+35-\left(w+1\right)\times 6=-7$$

w+1 ga 6 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-5w^{2}+30w+35-\left(6w+6\right)=-7$$

6w+6 teskarisini topish uchun har birining teskarisini toping.

$$-5w^{2}+30w+35-6w-6=-7$$

24w ni olish uchun 30w va -6w ni birlashtirish.

$$-5w^{2}+24w+35-6=-7$$

29 olish uchun 35 dan 6 ni ayirish.

$$-5w^{2}+24w+29=-7$$

Ikkala tarafdan 29 ni ayirish.

$$-5w^{2}+24w=-7-29$$

-36 olish uchun -7 dan 29 ni ayirish.

$$-5w^{2}+24w=-36$$

Ikki tarafini -5 ga bo‘ling.

$$\frac{-5w^{2}+24w}{-5}=-\frac{36}{-5}$$

-5 ga bo'lish -5 ga ko'paytirishni bekor qiladi.

$$w^{2}+\frac{24}{-5}w=-\frac{36}{-5}$$

24 ni -5 ga bo'lish.

$$w^{2}-\frac{24}{5}w=-\frac{36}{-5}$$

-36 ni -5 ga bo'lish.

$$w^{2}-\frac{24}{5}w=\frac{36}{5}$$

-\frac{24}{5} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{12}{5} olish uchun. Keyin, -\frac{12}{5} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$w^{2}-\frac{24}{5}w+\left(-\frac{12}{5}\right)^{2}=\frac{36}{5}+\left(-\frac{12}{5}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{12}{5} kvadratini chiqarish.

$$w^{2}-\frac{24}{5}w+\frac{144}{25}=\frac{36}{5}+\frac{144}{25}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{36}{5} ni \frac{144}{25} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$w^{2}-\frac{24}{5}w+\frac{144}{25}=\frac{324}{25}$$

w^{2}-\frac{24}{5}w+\frac{144}{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.

$$\left(w-\frac{12}{5}\right)^{2}=\frac{324}{25}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(w-\frac{12}{5}\right)^{2}}=\sqrt{\frac{324}{25}}$$

Qisqartirish.

$$w-\frac{12}{5}=\frac{18}{5} w-\frac{12}{5}=-\frac{18}{5}$$

\frac{12}{5} ni tenglamaning ikkala tarafiga qo'shish.

$$w=6 w=-\frac{6}{5}$$