s^2-9s=0 eching

$$s ^ { 2 } - 9 s = 0$$

s uchun yechish

$$s=9$$

$$s=0$$

Faktorlash qadamlari

s omili.

$$s\left(s-9\right)=0$$

Tenglamani yechish uchun s=0 va s-9=0 ni yeching.

$$s=0 s=9$$

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.

$$s^{2}-9s=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -9 ni b va 0 ni c bilan almashtiring.

$$s=\frac{-\left(-9\right)±\sqrt{\left(-9\right)^{2}}}{2}$$

\left(-9\right)^{2} ning kvadrat ildizini chiqarish.

$$s=\frac{-\left(-9\right)±9}{2}$$

-9 ning teskarisi 9 ga teng.

$$s=\frac{9±9}{2}$$

s=\frac{9±9}{2} tenglamasini yeching, bunda ± musbat. 9 ni 9 ga qo'shish.

$$s=\frac{18}{2}$$

18 ni 2 ga bo'lish.

$$s=9$$

s=\frac{9±9}{2} tenglamasini yeching, bunda ± manfiy. 9 dan 9 ni ayirish.

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

0 ni 2 ga bo'lish.

$$s=0$$

Tenglama yechildi.

$$s=9 s=0$$

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.

$$s^{2}-9s=0$$

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

$$s^{2}-9s+\left(-\frac{9}{2}\right)^{2}=\left(-\frac{9}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{9}{2} kvadratini chiqarish.

$$s^{2}-9s+\frac{81}{4}=\frac{81}{4}$$

s^{2}-9s+\frac{81}{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.

$$\left(s-\frac{9}{2}\right)^{2}=\frac{81}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(s-\frac{9}{2}\right)^{2}}=\sqrt{\frac{81}{4}}$$

Qisqartirish.

$$s-\frac{9}{2}=\frac{9}{2} s-\frac{9}{2}=-\frac{9}{2}$$

\frac{9}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$s=9 s=0$$