v/12=-4/v+14 eching

$$\frac { v } { 12 } = \frac { - 4 } { v + 14 }$$

v uchun yechish

$$v=-8$$

$$v=-6$$

Kvadrat tenglamalaridan foydalanish qoidalari

v qiymati -14 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 12\left(v+14\right) ga, 12,v+14 ning eng kichik karralisiga ko‘paytiring.

$$\left(v+14\right)v=12\left(-4\right)$$

v+14 ga v ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$v^{2}+14v=12\left(-4\right)$$

-48 hosil qilish uchun 12 va -4 ni ko'paytirish.

$$v^{2}+14v=-48$$

48 ni ikki tarafga qo’shing.

$$v^{2}+14v+48=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 14 ni b va 48 ni c bilan almashtiring.

$$v=\frac{-14±\sqrt{14^{2}-4\times 48}}{2}$$

14 kvadratini chiqarish.

$$v=\frac{-14±\sqrt{196-4\times 48}}{2}$$

-4 ni 48 marotabaga ko'paytirish.

$$v=\frac{-14±\sqrt{196-192}}{2}$$

196 ni -192 ga qo'shish.

$$v=\frac{-14±\sqrt{4}}{2}$$

4 ning kvadrat ildizini chiqarish.

$$v=\frac{-14±2}{2}$$

v=\frac{-14±2}{2} tenglamasini yeching, bunda ± musbat. -14 ni 2 ga qo'shish.

$$v=-\frac{12}{2}$$

-12 ni 2 ga bo'lish.

$$v=-6$$

v=\frac{-14±2}{2} tenglamasini yeching, bunda ± manfiy. -14 dan 2 ni ayirish.

$$v=-\frac{16}{2}$$

-16 ni 2 ga bo'lish.

$$v=-8$$

Tenglama yechildi.

$$v=-6 v=-8$$

Kvadratni yakunlash bo'yicha qadamlar

v qiymati -14 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 12\left(v+14\right) ga, 12,v+14 ning eng kichik karralisiga ko‘paytiring.

$$\left(v+14\right)v=12\left(-4\right)$$

v+14 ga v ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$v^{2}+14v=12\left(-4\right)$$

-48 hosil qilish uchun 12 va -4 ni ko'paytirish.

$$v^{2}+14v=-48$$

14 ni bo‘lish, x shartining koeffitsienti, 2 ga 7 olish uchun. Keyin, 7 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$v^{2}+14v+7^{2}=-48+7^{2}$$

7 kvadratini chiqarish.

$$v^{2}+14v+49=-48+49$$

-48 ni 49 ga qo'shish.

$$v^{2}+14v+49=1$$

v^{2}+14v+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.

$$\left(v+7\right)^{2}=1$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(v+7\right)^{2}}=\sqrt{1}$$

Qisqartirish.

$$v+7=1 v+7=-1$$

Tenglamaning ikkala tarafidan 7 ni ayirish.

$$v=-6 v=-8$$