3x(1+8x)=0 eching

$$3 x ( 1 + 8 x ) = 0$$

x uchun yechish

$$x=-\frac{1}{8}=-0,125$$

$$x=0$$

Faktorlash qadamlari

3x ga 1+8x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3x+24x^{2}=0$$

x omili.

$$x\left(3+24x\right)=0$$

Tenglamani yechish uchun x=0 va 3+24x=0 ni yeching.

$$x=0 x=-\frac{1}{8}$$

Kvadrat tenglamalaridan foydalanish qoidalari

3x ga 1+8x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3x+24x^{2}=0$$

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.

$$24x^{2}+3x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 24 ni a, 3 ni b va 0 ni c bilan almashtiring.

$$x=\frac{-3±\sqrt{3^{2}}}{2\times 24}$$

3^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-3±3}{2\times 24}$$

2 ni 24 marotabaga ko'paytirish.

$$x=\frac{-3±3}{48}$$

x=\frac{-3±3}{48} tenglamasini yeching, bunda ± musbat. -3 ni 3 ga qo'shish.

$$x=\frac{0}{48}$$

0 ni 48 ga bo'lish.

$$x=0$$

x=\frac{-3±3}{48} tenglamasini yeching, bunda ± manfiy. -3 dan 3 ni ayirish.

$$x=-\frac{6}{48}$$

\frac{-6}{48} ulushini 6 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=-\frac{1}{8}$$

Tenglama yechildi.

$$x=0 x=-\frac{1}{8}$$

Kvadratni yakunlash bo'yicha qadamlar

3x ga 1+8x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3x+24x^{2}=0$$

Bu kabi kvadrat tenglamalarni kvadratni yakunlab yechish mumkin. Kvadratni yechish uchun tenglama avval ushbu shaklda bo'lishi shart: x^{2}+bx=c.

$$24x^{2}+3x=0$$

Ikki tarafini 24 ga bo‘ling.

$$\frac{24x^{2}+3x}{24}=\frac{0}{24}$$

24 ga bo'lish 24 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{3}{24}x=\frac{0}{24}$$

\frac{3}{24} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}+\frac{1}{8}x=\frac{0}{24}$$

0 ni 24 ga bo'lish.

$$x^{2}+\frac{1}{8}x=0$$

\frac{1}{8} ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{1}{16} olish uchun. Keyin, \frac{1}{16} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+\frac{1}{8}x+\left(\frac{1}{16}\right)^{2}=\left(\frac{1}{16}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{1}{16} kvadratini chiqarish.

$$x^{2}+\frac{1}{8}x+\frac{1}{256}=\frac{1}{256}$$

x^{2}+\frac{1}{8}x+\frac{1}{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.

$$\left(x+\frac{1}{16}\right)^{2}=\frac{1}{256}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{1}{16}\right)^{2}}=\sqrt{\frac{1}{256}}$$

Qisqartirish.

$$x+\frac{1}{16}=\frac{1}{16} x+\frac{1}{16}=-\frac{1}{16}$$

Tenglamaning ikkala tarafidan \frac{1}{16} ni ayirish.

$$x=0 x=-\frac{1}{8}$$