5x^2+3x=0 eching

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

x uchun yechish

$$x=-\frac{3}{5}=-0,6$$

$$x=0$$

Faktorlash qadamlari

x omili.

$$x\left(5x+3\right)=0$$

Tenglamani yechish uchun x=0 va 5x+3=0 ni yeching.

$$x=0 x=-\frac{3}{5}$$

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.

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

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

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

3^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-3±3}{2\times 5}$$

2 ni 5 marotabaga ko'paytirish.

$$x=\frac{-3±3}{10}$$

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

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

0 ni 10 ga bo'lish.

$$x=0$$

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

$$x=-\frac{6}{10}$$

\frac{-6}{10} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

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

Tenglama yechildi.

$$x=0 x=-\frac{3}{5}$$

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.

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

Ikki tarafini 5 ga bo‘ling.

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

5 ga bo'lish 5 ga ko'paytirishni bekor qiladi.

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

0 ni 5 ga bo'lish.

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

\frac{3}{5} ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{3}{10} olish uchun. Keyin, \frac{3}{10} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+\frac{3}{5}x+\left(\frac{3}{10}\right)^{2}=\left(\frac{3}{10}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{3}{10} kvadratini chiqarish.

$$x^{2}+\frac{3}{5}x+\frac{9}{100}=\frac{9}{100}$$

x^{2}+\frac{3}{5}x+\frac{9}{100} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+\frac{3}{10}\right)^{2}=\frac{9}{100}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{3}{10}\right)^{2}}=\sqrt{\frac{9}{100}}$$

Qisqartirish.

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

Tenglamaning ikkala tarafidan \frac{3}{10} ni ayirish.

$$x=0 x=-\frac{3}{5}$$