-12+8/w=w+35/w eching

$$- 12 + \frac { 8 } { w } = w + \frac { 35 } { w }$$

w uchun yechish

$$w=-9$$

$$w=-3$$

Kvadrat tenglamalaridan foydalanish qoidalari

w qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini w ga ko'paytirish.

$$w\left(-12\right)+8=ww+35$$

w^{2} hosil qilish uchun w va w ni ko'paytirish.

$$w\left(-12\right)+8=w^{2}+35$$

Ikkala tarafdan w^{2} ni ayirish.

$$w\left(-12\right)+8-w^{2}=35$$

Ikkala tarafdan 35 ni ayirish.

$$w\left(-12\right)+8-w^{2}-35=0$$

-27 olish uchun 8 dan 35 ni ayirish.

$$w\left(-12\right)-27-w^{2}=0$$

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.

$$-w^{2}-12w-27=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -1 ni a, -12 ni b va -27 ni c bilan almashtiring.

$$w=\frac{-\left(-12\right)±\sqrt{\left(-12\right)^{2}-4\left(-1\right)\left(-27\right)}}{2\left(-1\right)}$$

-12 kvadratini chiqarish.

$$w=\frac{-\left(-12\right)±\sqrt{144-4\left(-1\right)\left(-27\right)}}{2\left(-1\right)}$$

-4 ni -1 marotabaga ko'paytirish.

$$w=\frac{-\left(-12\right)±\sqrt{144+4\left(-27\right)}}{2\left(-1\right)}$$

4 ni -27 marotabaga ko'paytirish.

$$w=\frac{-\left(-12\right)±\sqrt{144-108}}{2\left(-1\right)}$$

144 ni -108 ga qo'shish.

$$w=\frac{-\left(-12\right)±\sqrt{36}}{2\left(-1\right)}$$

36 ning kvadrat ildizini chiqarish.

$$w=\frac{-\left(-12\right)±6}{2\left(-1\right)}$$

-12 ning teskarisi 12 ga teng.

$$w=\frac{12±6}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$w=\frac{12±6}{-2}$$

w=\frac{12±6}{-2} tenglamasini yeching, bunda ± musbat. 12 ni 6 ga qo'shish.

$$w=\frac{18}{-2}$$

18 ni -2 ga bo'lish.

$$w=-9$$

w=\frac{12±6}{-2} tenglamasini yeching, bunda ± manfiy. 12 dan 6 ni ayirish.

$$w=\frac{6}{-2}$$

6 ni -2 ga bo'lish.

$$w=-3$$

Tenglama yechildi.

$$w=-9 w=-3$$

Kvadratni yakunlash bo'yicha qadamlar

w qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini w ga ko'paytirish.

$$w\left(-12\right)+8=ww+35$$

w^{2} hosil qilish uchun w va w ni ko'paytirish.

$$w\left(-12\right)+8=w^{2}+35$$

Ikkala tarafdan w^{2} ni ayirish.

$$w\left(-12\right)+8-w^{2}=35$$

Ikkala tarafdan 8 ni ayirish.

$$w\left(-12\right)-w^{2}=35-8$$

27 olish uchun 35 dan 8 ni ayirish.

$$w\left(-12\right)-w^{2}=27$$

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

$$-w^{2}-12w=27$$

Ikki tarafini -1 ga bo‘ling.

$$\frac{-w^{2}-12w}{-1}=\frac{27}{-1}$$

-1 ga bo'lish -1 ga ko'paytirishni bekor qiladi.

$$w^{2}+\left(-\frac{12}{-1}\right)w=\frac{27}{-1}$$

-12 ni -1 ga bo'lish.

$$w^{2}+12w=\frac{27}{-1}$$

27 ni -1 ga bo'lish.

$$w^{2}+12w=-27$$

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

$$w^{2}+12w+6^{2}=-27+6^{2}$$

6 kvadratini chiqarish.

$$w^{2}+12w+36=-27+36$$

-27 ni 36 ga qo'shish.

$$w^{2}+12w+36=9$$

w^{2}+12w+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.

$$\left(w+6\right)^{2}=9$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(w+6\right)^{2}}=\sqrt{9}$$

Qisqartirish.

$$w+6=3 w+6=-3$$

Tenglamaning ikkala tarafidan 6 ni ayirish.

$$w=-3 w=-9$$