1/w=w+2/35 eching

$$\frac { 1 } { w } = \frac { w + 2 } { 35 }$$

w uchun yechish

$$w=-7$$

$$w=5$$

Kvadrat tenglamalaridan foydalanish qoidalari

w qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 35w ga, w,35 ning eng kichik karralisiga ko‘paytiring.

$$35=w\left(w+2\right)$$

w ga w+2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$35=w^{2}+2w$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$w^{2}+2w=35$$

Ikkala tarafdan 35 ni ayirish.

$$w^{2}+2w-35=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 2 ni b va -35 ni c bilan almashtiring.

$$w=\frac{-2±\sqrt{2^{2}-4\left(-35\right)}}{2}$$

2 kvadratini chiqarish.

$$w=\frac{-2±\sqrt{4-4\left(-35\right)}}{2}$$

-4 ni -35 marotabaga ko'paytirish.

$$w=\frac{-2±\sqrt{4+140}}{2}$$

4 ni 140 ga qo'shish.

$$w=\frac{-2±\sqrt{144}}{2}$$

144 ning kvadrat ildizini chiqarish.

$$w=\frac{-2±12}{2}$$

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

$$w=\frac{10}{2}$$

10 ni 2 ga bo'lish.

$$w=5$$

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

$$w=-\frac{14}{2}$$

-14 ni 2 ga bo'lish.

$$w=-7$$

Tenglama yechildi.

$$w=5 w=-7$$

Kvadratni yakunlash bo'yicha qadamlar

w qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 35w ga, w,35 ning eng kichik karralisiga ko‘paytiring.

$$35=w\left(w+2\right)$$

w ga w+2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$35=w^{2}+2w$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$w^{2}+2w=35$$

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

$$w^{2}+2w+1^{2}=35+1^{2}$$

1 kvadratini chiqarish.

$$w^{2}+2w+1=35+1$$

35 ni 1 ga qo'shish.

$$w^{2}+2w+1=36$$

w^{2}+2w+1 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(w+1\right)^{2}=36$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(w+1\right)^{2}}=\sqrt{36}$$

Qisqartirish.

$$w+1=6 w+1=-6$$

Tenglamaning ikkala tarafidan 1 ni ayirish.

$$w=5 w=-7$$