4x^2+2x/3=0 eching

$$4 { x }^{ 2 } + \frac{ 2x }{ 3 } =0$$

x uchun yechish

$$x=-\frac{1}{6}\approx -0,166666667$$

$$x=0$$

Faktorlash qadamlari

Tenglamaning ikkala tarafini 3 ga ko'paytirish.

$$12x^{2}+2x=0$$

x omili.

$$x\left(12x+2\right)=0$$

Tenglamani yechish uchun x=0 va 12x+2=0 ni yeching.

$$x=0 x=-\frac{1}{6}$$

Kvadrat tenglamalaridan foydalanish qoidalari

Tenglamaning ikkala tarafini 3 ga ko'paytirish.

$$12x^{2}+2x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 12 ni a, 2 ni b va 0 ni c bilan almashtiring.

$$x=\frac{-2±\sqrt{2^{2}}}{2\times 12}$$

2^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-2±2}{2\times 12}$$

2 ni 12 marotabaga ko'paytirish.

$$x=\frac{-2±2}{24}$$

x=\frac{-2±2}{24} tenglamasini yeching, bunda ± musbat. -2 ni 2 ga qo'shish.

$$x=\frac{0}{24}$$

0 ni 24 ga bo'lish.

$$x=0$$

x=\frac{-2±2}{24} tenglamasini yeching, bunda ± manfiy. -2 dan 2 ni ayirish.

$$x=-\frac{4}{24}$$

\frac{-4}{24} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=-\frac{1}{6}$$

Tenglama yechildi.

$$x=0 x=-\frac{1}{6}$$

Kvadratni yakunlash bo'yicha qadamlar

Tenglamaning ikkala tarafini 3 ga ko'paytirish.

$$12x^{2}+2x=0$$

Ikki tarafini 12 ga bo‘ling.

$$\frac{12x^{2}+2x}{12}=\frac{0}{12}$$

12 ga bo'lish 12 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{2}{12}x=\frac{0}{12}$$

\frac{2}{12} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}+\frac{1}{6}x=\frac{0}{12}$$

0 ni 12 ga bo'lish.

$$x^{2}+\frac{1}{6}x=0$$

\frac{1}{6} ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{1}{12} olish uchun. Keyin, \frac{1}{12} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+\frac{1}{6}x+\left(\frac{1}{12}\right)^{2}=\left(\frac{1}{12}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{1}{12} kvadratini chiqarish.

$$x^{2}+\frac{1}{6}x+\frac{1}{144}=\frac{1}{144}$$

x^{2}+\frac{1}{6}x+\frac{1}{144} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+\frac{1}{12}\right)^{2}=\frac{1}{144}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{1}{12}\right)^{2}}=\sqrt{\frac{1}{144}}$$

Qisqartirish.

$$x+\frac{1}{12}=\frac{1}{12} x+\frac{1}{12}=-\frac{1}{12}$$

Tenglamaning ikkala tarafidan \frac{1}{12} ni ayirish.

$$x=0 x=-\frac{1}{6}$$