5p^2=35p eching

$$5 p ^ { 2 } = 35 p$$

p uchun yechish

$$p=7$$

$$p=0$$

Faktorlash qadamlari

Ikkala tarafdan 35p ni ayirish.

$$5p^{2}-35p=0$$

p omili.

$$p\left(5p-35\right)=0$$

Tenglamani yechish uchun p=0 va 5p-35=0 ni yeching.

$$p=0 p=7$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 35p ni ayirish.

$$5p^{2}-35p=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 5 ni a, -35 ni b va 0 ni c bilan almashtiring.

$$p=\frac{-\left(-35\right)±\sqrt{\left(-35\right)^{2}}}{2\times 5}$$

\left(-35\right)^{2} ning kvadrat ildizini chiqarish.

$$p=\frac{-\left(-35\right)±35}{2\times 5}$$

-35 ning teskarisi 35 ga teng.

$$p=\frac{35±35}{2\times 5}$$

2 ni 5 marotabaga ko'paytirish.

$$p=\frac{35±35}{10}$$

p=\frac{35±35}{10} tenglamasini yeching, bunda ± musbat. 35 ni 35 ga qo'shish.

$$p=\frac{70}{10}$$

70 ni 10 ga bo'lish.

$$p=7$$

p=\frac{35±35}{10} tenglamasini yeching, bunda ± manfiy. 35 dan 35 ni ayirish.

$$p=\frac{0}{10}$$

0 ni 10 ga bo'lish.

$$p=0$$

Tenglama yechildi.

$$p=7 p=0$$

Kvadratni yakunlash bo'yicha qadamlar

Ikkala tarafdan 35p ni ayirish.

$$5p^{2}-35p=0$$

Ikki tarafini 5 ga bo‘ling.

$$\frac{5p^{2}-35p}{5}=\frac{0}{5}$$

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

$$p^{2}+\left(-\frac{35}{5}\right)p=\frac{0}{5}$$

-35 ni 5 ga bo'lish.

$$p^{2}-7p=\frac{0}{5}$$

0 ni 5 ga bo'lish.

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

-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.

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

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

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

p^{2}-7p+\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.

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

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

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

Qisqartirish.

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

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

$$p=7 p=0$$