2v(v-7)=5v(v-7) eching

$$2 v ( v - 7 ) = 5 v ( v - 7 )$$

v uchun yechish

$$v=7$$

$$v=0$$

Faktorlash qadamlari

2v ga v-7 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$2v^{2}-14v=5v\left(v-7\right)$$

5v ga v-7 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$2v^{2}-14v=5v^{2}-35v$$

Ikkala tarafdan 5v^{2} ni ayirish.

$$2v^{2}-14v-5v^{2}=-35v$$

-3v^{2} ni olish uchun 2v^{2} va -5v^{2} ni birlashtirish.

$$-3v^{2}-14v=-35v$$

35v ni ikki tarafga qo’shing.

$$-3v^{2}-14v+35v=0$$

21v ni olish uchun -14v va 35v ni birlashtirish.

$$-3v^{2}+21v=0$$

v omili.

$$v\left(-3v+21\right)=0$$

Tenglamani yechish uchun v=0 va -3v+21=0 ni yeching.

$$v=0 v=7$$

Kvadrat tenglamalaridan foydalanish qoidalari

2v ga v-7 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$2v^{2}-14v=5v\left(v-7\right)$$

5v ga v-7 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$2v^{2}-14v=5v^{2}-35v$$

Ikkala tarafdan 5v^{2} ni ayirish.

$$2v^{2}-14v-5v^{2}=-35v$$

-3v^{2} ni olish uchun 2v^{2} va -5v^{2} ni birlashtirish.

$$-3v^{2}-14v=-35v$$

35v ni ikki tarafga qo’shing.

$$-3v^{2}-14v+35v=0$$

21v ni olish uchun -14v va 35v ni birlashtirish.

$$-3v^{2}+21v=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -3 ni a, 21 ni b va 0 ni c bilan almashtiring.

$$v=\frac{-21±\sqrt{21^{2}}}{2\left(-3\right)}$$

21^{2} ning kvadrat ildizini chiqarish.

$$v=\frac{-21±21}{2\left(-3\right)}$$

2 ni -3 marotabaga ko'paytirish.

$$v=\frac{-21±21}{-6}$$

v=\frac{-21±21}{-6} tenglamasini yeching, bunda ± musbat. -21 ni 21 ga qo'shish.

$$v=\frac{0}{-6}$$

0 ni -6 ga bo'lish.

$$v=0$$

v=\frac{-21±21}{-6} tenglamasini yeching, bunda ± manfiy. -21 dan 21 ni ayirish.

$$v=-\frac{42}{-6}$$

-42 ni -6 ga bo'lish.

$$v=7$$

Tenglama yechildi.

$$v=0 v=7$$

Kvadratni yakunlash bo'yicha qadamlar

2v ga v-7 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$2v^{2}-14v=5v\left(v-7\right)$$

5v ga v-7 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$2v^{2}-14v=5v^{2}-35v$$

Ikkala tarafdan 5v^{2} ni ayirish.

$$2v^{2}-14v-5v^{2}=-35v$$

-3v^{2} ni olish uchun 2v^{2} va -5v^{2} ni birlashtirish.

$$-3v^{2}-14v=-35v$$

35v ni ikki tarafga qo’shing.

$$-3v^{2}-14v+35v=0$$

21v ni olish uchun -14v va 35v ni birlashtirish.

$$-3v^{2}+21v=0$$

Ikki tarafini -3 ga bo‘ling.

$$\frac{-3v^{2}+21v}{-3}=\frac{0}{-3}$$

-3 ga bo'lish -3 ga ko'paytirishni bekor qiladi.

$$v^{2}+\frac{21}{-3}v=\frac{0}{-3}$$

21 ni -3 ga bo'lish.

$$v^{2}-7v=\frac{0}{-3}$$

0 ni -3 ga bo'lish.

$$v^{2}-7v=0$$

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

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

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{7}{2} kvadratini chiqarish.

$$v^{2}-7v+\frac{49}{4}=\frac{49}{4}$$

v^{2}-7v+\frac{49}{4} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(v-\frac{7}{2}\right)^{2}=\frac{49}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(v-\frac{7}{2}\right)^{2}}=\sqrt{\frac{49}{4}}$$

Qisqartirish.

$$v-\frac{7}{2}=\frac{7}{2} v-\frac{7}{2}=-\frac{7}{2}$$

\frac{7}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$v=7 v=0$$