8s^2+9s+2=0 eching

$$8 s ^ { 2 } + 9 s + 2 = 0$$

s uchun yechish

$$s=\frac{\sqrt{17}-9}{16}\approx -0,304805898$$

$$s=\frac{-\sqrt{17}-9}{16}\approx -0,820194102$$

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.

$$8s^{2}+9s+2=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 8 ni a, 9 ni b va 2 ni c bilan almashtiring.

$$s=\frac{-9±\sqrt{9^{2}-4\times 8\times 2}}{2\times 8}$$

9 kvadratini chiqarish.

$$s=\frac{-9±\sqrt{81-4\times 8\times 2}}{2\times 8}$$

-4 ni 8 marotabaga ko'paytirish.

$$s=\frac{-9±\sqrt{81-32\times 2}}{2\times 8}$$

-32 ni 2 marotabaga ko'paytirish.

$$s=\frac{-9±\sqrt{81-64}}{2\times 8}$$

81 ni -64 ga qo'shish.

$$s=\frac{-9±\sqrt{17}}{2\times 8}$$

2 ni 8 marotabaga ko'paytirish.

$$s=\frac{-9±\sqrt{17}}{16}$$

s=\frac{-9±\sqrt{17}}{16} tenglamasini yeching, bunda ± musbat. -9 ni \sqrt{17} ga qo'shish.

$$s=\frac{\sqrt{17}-9}{16}$$

s=\frac{-9±\sqrt{17}}{16} tenglamasini yeching, bunda ± manfiy. -9 dan \sqrt{17} ni ayirish.

$$s=\frac{-\sqrt{17}-9}{16}$$

Tenglama yechildi.

$$s=\frac{\sqrt{17}-9}{16} s=\frac{-\sqrt{17}-9}{16}$$

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.

$$8s^{2}+9s+2=0$$

Tenglamaning ikkala tarafidan 2 ni ayirish.

$$8s^{2}+9s+2-2=-2$$

O‘zidan 2 ayirilsa 0 qoladi.

$$8s^{2}+9s=-2$$

Ikki tarafini 8 ga bo‘ling.

$$\frac{8s^{2}+9s}{8}=-\frac{2}{8}$$

8 ga bo'lish 8 ga ko'paytirishni bekor qiladi.

$$s^{2}+\frac{9}{8}s=-\frac{2}{8}$$

\frac{-2}{8} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$s^{2}+\frac{9}{8}s=-\frac{1}{4}$$

\frac{9}{8} ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{9}{16} olish uchun. Keyin, \frac{9}{16} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$s^{2}+\frac{9}{8}s+\left(\frac{9}{16}\right)^{2}=-\frac{1}{4}+\left(\frac{9}{16}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{9}{16} kvadratini chiqarish.

$$s^{2}+\frac{9}{8}s+\frac{81}{256}=-\frac{1}{4}+\frac{81}{256}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali -\frac{1}{4} ni \frac{81}{256} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$s^{2}+\frac{9}{8}s+\frac{81}{256}=\frac{17}{256}$$

s^{2}+\frac{9}{8}s+\frac{81}{256} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(s+\frac{9}{16}\right)^{2}=\frac{17}{256}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(s+\frac{9}{16}\right)^{2}}=\sqrt{\frac{17}{256}}$$

Qisqartirish.

$$s+\frac{9}{16}=\frac{\sqrt{17}}{16} s+\frac{9}{16}=-\frac{\sqrt{17}}{16}$$

Tenglamaning ikkala tarafidan \frac{9}{16} ni ayirish.

$$s=\frac{\sqrt{17}-9}{16} s=\frac{-\sqrt{17}-9}{16}$$