p^2-18p=0 eching

$$p ^ { 2 } - 18 p = 0$$

p uchun yechish

$$p=18$$

$$p=0$$

Faktorlash qadamlari

p omili.

$$p\left(p-18\right)=0$$

Tenglamani yechish uchun p=0 va p-18=0 ni yeching.

$$p=0 p=18$$

Kvadrat tenglamalaridan foydalanish qoidalari

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.

$$p^{2}-18p=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -18 ni b va 0 ni c bilan almashtiring.

$$p=\frac{-\left(-18\right)±\sqrt{\left(-18\right)^{2}}}{2}$$

\left(-18\right)^{2} ning kvadrat ildizini chiqarish.

$$p=\frac{-\left(-18\right)±18}{2}$$

-18 ning teskarisi 18 ga teng.

$$p=\frac{18±18}{2}$$

p=\frac{18±18}{2} tenglamasini yeching, bunda ± musbat. 18 ni 18 ga qo'shish.

$$p=\frac{36}{2}$$

36 ni 2 ga bo'lish.

$$p=18$$

p=\frac{18±18}{2} tenglamasini yeching, bunda ± manfiy. 18 dan 18 ni ayirish.

$$p=\frac{0}{2}$$

0 ni 2 ga bo'lish.

$$p=0$$

Tenglama yechildi.

$$p=18 p=0$$

Kvadratni yakunlash bo'yicha qadamlar

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

$$p^{2}-18p=0$$

-18 ni bo‘lish, x shartining koeffitsienti, 2 ga -9 olish uchun. Keyin, -9 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$p^{2}-18p+\left(-9\right)^{2}=\left(-9\right)^{2}$$

-9 kvadratini chiqarish.

$$p^{2}-18p+81=81$$

p^{2}-18p+81 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(p-9\right)^{2}=81$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(p-9\right)^{2}}=\sqrt{81}$$

Qisqartirish.

$$p-9=9 p-9=-9$$

9 ni tenglamaning ikkala tarafiga qo'shish.

$$p=18 p=0$$