5/3x^2+2x=0 eching

$$\frac { 5 } { 3 } x ^ { 2 } + 2 x = 0$$

x uchun yechish

$$x = -\frac{6}{5} = -1\frac{1}{5} = -1,2$$

$$x=0$$

Faktorlash qadamlari

x omili.

$$x\left(\frac{5}{3}x+2\right)=0$$

Tenglamani yechish uchun x=0 va \frac{5x}{3}+2=0 ni yeching.

$$x=0 x=-\frac{6}{5}$$

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.

$$\frac{5}{3}x^{2}+2x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} \frac{5}{3} ni a, 2 ni b va 0 ni c bilan almashtiring.

$$x=\frac{-2±\sqrt{2^{2}}}{2\times \frac{5}{3}}$$

2^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-2±2}{2\times \frac{5}{3}}$$

2 ni \frac{5}{3} marotabaga ko'paytirish.

$$x=\frac{-2±2}{\frac{10}{3}}$$

x=\frac{-2±2}{\frac{10}{3}} tenglamasini yeching, bunda ± musbat. -2 ni 2 ga qo'shish.

$$x=\frac{0}{\frac{10}{3}}$$

0 ni \frac{10}{3} ga bo'lish 0 ga k'paytirish \frac{10}{3} ga qaytarish.

$$x=0$$

x=\frac{-2±2}{\frac{10}{3}} tenglamasini yeching, bunda ± manfiy. -2 dan 2 ni ayirish.

$$x=-\frac{4}{\frac{10}{3}}$$

-4 ni \frac{10}{3} ga bo'lish -4 ga k'paytirish \frac{10}{3} ga qaytarish.

$$x=-\frac{6}{5}$$

Tenglama yechildi.

$$x=0 x=-\frac{6}{5}$$

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.

$$\frac{5}{3}x^{2}+2x=0$$

Tenglamaning ikki tarafini \frac{5}{3} ga bo'lish, bu kasrni qaytarish orqali ikkala tarafga ko'paytirish bilan aynidir.

$$\frac{\frac{5}{3}x^{2}+2x}{\frac{5}{3}}=\frac{0}{\frac{5}{3}}$$

\frac{5}{3} ga bo'lish \frac{5}{3} ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{2}{\frac{5}{3}}x=\frac{0}{\frac{5}{3}}$$

2 ni \frac{5}{3} ga bo'lish 2 ga k'paytirish \frac{5}{3} ga qaytarish.

$$x^{2}+\frac{6}{5}x=\frac{0}{\frac{5}{3}}$$

0 ni \frac{5}{3} ga bo'lish 0 ga k'paytirish \frac{5}{3} ga qaytarish.

$$x^{2}+\frac{6}{5}x=0$$

\frac{6}{5} ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{3}{5} olish uchun. Keyin, \frac{3}{5} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+\frac{6}{5}x+\left(\frac{3}{5}\right)^{2}=\left(\frac{3}{5}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{3}{5} kvadratini chiqarish.

$$x^{2}+\frac{6}{5}x+\frac{9}{25}=\frac{9}{25}$$

x^{2}+\frac{6}{5}x+\frac{9}{25} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+\frac{3}{5}\right)^{2}=\frac{9}{25}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{3}{5}\right)^{2}}=\sqrt{\frac{9}{25}}$$

Qisqartirish.

$$x+\frac{3}{5}=\frac{3}{5} x+\frac{3}{5}=-\frac{3}{5}$$

Tenglamaning ikkala tarafidan \frac{3}{5} ni ayirish.

$$x=0 x=-\frac{6}{5}$$