2s^2+6s+2=0 eching

$$2 s ^ { 2 } + 6 s + 2 = 0$$

s uchun yechish

$$s=\frac{\sqrt{5}-3}{2}\approx -0,381966011$$

$$s=\frac{-\sqrt{5}-3}{2}\approx -2,618033989$$

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.

$$2s^{2}+6s+2=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 2 ni a, 6 ni b va 2 ni c bilan almashtiring.

$$s=\frac{-6±\sqrt{6^{2}-4\times 2\times 2}}{2\times 2}$$

6 kvadratini chiqarish.

$$s=\frac{-6±\sqrt{36-4\times 2\times 2}}{2\times 2}$$

-4 ni 2 marotabaga ko'paytirish.

$$s=\frac{-6±\sqrt{36-8\times 2}}{2\times 2}$$

-8 ni 2 marotabaga ko'paytirish.

$$s=\frac{-6±\sqrt{36-16}}{2\times 2}$$

36 ni -16 ga qo'shish.

$$s=\frac{-6±\sqrt{20}}{2\times 2}$$

20 ning kvadrat ildizini chiqarish.

$$s=\frac{-6±2\sqrt{5}}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$s=\frac{-6±2\sqrt{5}}{4}$$

s=\frac{-6±2\sqrt{5}}{4} tenglamasini yeching, bunda ± musbat. -6 ni 2\sqrt{5} ga qo'shish.

$$s=\frac{2\sqrt{5}-6}{4}$$

-6+2\sqrt{5} ni 4 ga bo'lish.

$$s=\frac{\sqrt{5}-3}{2}$$

s=\frac{-6±2\sqrt{5}}{4} tenglamasini yeching, bunda ± manfiy. -6 dan 2\sqrt{5} ni ayirish.

$$s=\frac{-2\sqrt{5}-6}{4}$$

-6-2\sqrt{5} ni 4 ga bo'lish.

$$s=\frac{-\sqrt{5}-3}{2}$$

Tenglama yechildi.

$$s=\frac{\sqrt{5}-3}{2} s=\frac{-\sqrt{5}-3}{2}$$

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.

$$2s^{2}+6s+2=0$$

Tenglamaning ikkala tarafidan 2 ni ayirish.

$$2s^{2}+6s+2-2=-2$$

O‘zidan 2 ayirilsa 0 qoladi.

$$2s^{2}+6s=-2$$

Ikki tarafini 2 ga bo‘ling.

$$\frac{2s^{2}+6s}{2}=-\frac{2}{2}$$

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

$$s^{2}+\frac{6}{2}s=-\frac{2}{2}$$

6 ni 2 ga bo'lish.

$$s^{2}+3s=-\frac{2}{2}$$

-2 ni 2 ga bo'lish.

$$s^{2}+3s=-1$$

3 ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{3}{2} olish uchun. Keyin, \frac{3}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$s^{2}+3s+\left(\frac{3}{2}\right)^{2}=-1+\left(\frac{3}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{3}{2} kvadratini chiqarish.

$$s^{2}+3s+\frac{9}{4}=-1+\frac{9}{4}$$

-1 ni \frac{9}{4} ga qo'shish.

$$s^{2}+3s+\frac{9}{4}=\frac{5}{4}$$

s^{2}+3s+\frac{9}{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.

$$\left(s+\frac{3}{2}\right)^{2}=\frac{5}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(s+\frac{3}{2}\right)^{2}}=\sqrt{\frac{5}{4}}$$

Qisqartirish.

$$s+\frac{3}{2}=\frac{\sqrt{5}}{2} s+\frac{3}{2}=-\frac{\sqrt{5}}{2}$$

Tenglamaning ikkala tarafidan \frac{3}{2} ni ayirish.

$$s=\frac{\sqrt{5}-3}{2} s=\frac{-\sqrt{5}-3}{2}$$