3x^2+11x-014=0 eching

$$3 { x }^{ 2 } +11x-014=0$$

x uchun yechish

$$x = -\frac{11}{3} = -3\frac{2}{3} \approx -3,666666667$$

$$x=0$$

Faktorlash qadamlari

0 hosil qilish uchun 0 va 14 ni ko'paytirish.

$$3x^{2}+11x-0=0$$

Shartlarni qayta saralash.

$$3x^{2}+11x=0$$

x omili.

$$x\left(3x+11\right)=0$$

Tenglamani yechish uchun x=0 va 3x+11=0 ni yeching.

$$x=0 x=-\frac{11}{3}$$

Kvadrat tenglamalaridan foydalanish qoidalari

0 hosil qilish uchun 0 va 14 ni ko'paytirish.

$$3x^{2}+11x-0=0$$

Shartlarni qayta saralash.

$$3x^{2}+11x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 3 ni a, 11 ni b va 0 ni c bilan almashtiring.

$$x=\frac{-11±\sqrt{11^{2}}}{2\times 3}$$

11^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-11±11}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$x=\frac{-11±11}{6}$$

x=\frac{-11±11}{6} tenglamasini yeching, bunda ± musbat. -11 ni 11 ga qo'shish.

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

0 ni 6 ga bo'lish.

$$x=0$$

x=\frac{-11±11}{6} tenglamasini yeching, bunda ± manfiy. -11 dan 11 ni ayirish.

$$x=-\frac{22}{6}$$

\frac{-22}{6} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=-\frac{11}{3}$$

Tenglama yechildi.

$$x=0 x=-\frac{11}{3}$$

Kvadratni yakunlash bo'yicha qadamlar

0 hosil qilish uchun 0 va 14 ni ko'paytirish.

$$3x^{2}+11x-0=0$$

0 ni ikki tarafga qo’shing.

$$3x^{2}+11x=0+0$$

0 olish uchun 0 va 0'ni qo'shing.

$$3x^{2}+11x=0$$

Ikki tarafini 3 ga bo‘ling.

$$\frac{3x^{2}+11x}{3}=\frac{0}{3}$$

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

$$x^{2}+\frac{11}{3}x=\frac{0}{3}$$

0 ni 3 ga bo'lish.

$$x^{2}+\frac{11}{3}x=0$$

\frac{11}{3} ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{11}{6} olish uchun. Keyin, \frac{11}{6} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+\frac{11}{3}x+\left(\frac{11}{6}\right)^{2}=\left(\frac{11}{6}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{11}{6} kvadratini chiqarish.

$$x^{2}+\frac{11}{3}x+\frac{121}{36}=\frac{121}{36}$$

x^{2}+\frac{11}{3}x+\frac{121}{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.

$$\left(x+\frac{11}{6}\right)^{2}=\frac{121}{36}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{11}{6}\right)^{2}}=\sqrt{\frac{121}{36}}$$

Qisqartirish.

$$x+\frac{11}{6}=\frac{11}{6} x+\frac{11}{6}=-\frac{11}{6}$$

Tenglamaning ikkala tarafidan \frac{11}{6} ni ayirish.

$$x=0 x=-\frac{11}{3}$$