2s^2-7s=0 eching

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

s uchun yechish

$$s = \frac{7}{2} = 3\frac{1}{2} = 3,5$$

$$s=0$$

Faktorlash qadamlari

s omili.

$$s\left(2s-7\right)=0$$

Tenglamani yechish uchun s=0 va 2s-7=0 ni yeching.

$$s=0 s=\frac{7}{2}$$

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.

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

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 2 ni a, -7 ni b va 0 ni c bilan almashtiring.

$$s=\frac{-\left(-7\right)±\sqrt{\left(-7\right)^{2}}}{2\times 2}$$

\left(-7\right)^{2} ning kvadrat ildizini chiqarish.

$$s=\frac{-\left(-7\right)±7}{2\times 2}$$

-7 ning teskarisi 7 ga teng.

$$s=\frac{7±7}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$s=\frac{7±7}{4}$$

s=\frac{7±7}{4} tenglamasini yeching, bunda ± musbat. 7 ni 7 ga qo'shish.

$$s=\frac{14}{4}$$

\frac{14}{4} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$s=\frac{7}{2}$$

s=\frac{7±7}{4} tenglamasini yeching, bunda ± manfiy. 7 dan 7 ni ayirish.

$$s=\frac{0}{4}$$

0 ni 4 ga bo'lish.

$$s=0$$

Tenglama yechildi.

$$s=\frac{7}{2} s=0$$

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.

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

Ikki tarafini 2 ga bo‘ling.

$$\frac{2s^{2}-7s}{2}=\frac{0}{2}$$

2 ga bo'lish 2 ga ko'paytirishni bekor qiladi.

$$s^{2}-\frac{7}{2}s=\frac{0}{2}$$

0 ni 2 ga bo'lish.

$$s^{2}-\frac{7}{2}s=0$$

-\frac{7}{2} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{7}{4} olish uchun. Keyin, -\frac{7}{4} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$s^{2}-\frac{7}{2}s+\left(-\frac{7}{4}\right)^{2}=\left(-\frac{7}{4}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{7}{4} kvadratini chiqarish.

$$s^{2}-\frac{7}{2}s+\frac{49}{16}=\frac{49}{16}$$

s^{2}-\frac{7}{2}s+\frac{49}{16} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(s-\frac{7}{4}\right)^{2}=\frac{49}{16}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(s-\frac{7}{4}\right)^{2}}=\sqrt{\frac{49}{16}}$$

Qisqartirish.

$$s-\frac{7}{4}=\frac{7}{4} s-\frac{7}{4}=-\frac{7}{4}$$

\frac{7}{4} ni tenglamaning ikkala tarafiga qo'shish.

$$s=\frac{7}{2} s=0$$