3x^2+5x=0 eching

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

x uchun yechish

$$x = -\frac{5}{3} = -1\frac{2}{3} \approx -1,666666667$$

$$x=0$$

Faktorlash qadamlari

x omili.

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

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

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

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.

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

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

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

5^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-5±5}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$x=\frac{-5±5}{6}$$

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

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

0 ni 6 ga bo'lish.

$$x=0$$

x=\frac{-5±5}{6} tenglamasini yeching, bunda ± manfiy. -5 dan 5 ni ayirish.

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

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

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

Tenglama yechildi.

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

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.

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

Ikki tarafini 3 ga bo‘ling.

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

3 ga bo'lish 3 ga ko'paytirishni bekor qiladi.

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

0 ni 3 ga bo'lish.

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

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

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

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{5}{6} kvadratini chiqarish.

$$x^{2}+\frac{5}{3}x+\frac{25}{36}=\frac{25}{36}$$

x^{2}+\frac{5}{3}x+\frac{25}{36} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+\frac{5}{6}\right)^{2}=\frac{25}{36}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{5}{6}\right)^{2}}=\sqrt{\frac{25}{36}}$$

Qisqartirish.

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

Tenglamaning ikkala tarafidan \frac{5}{6} ni ayirish.

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