30x^2+2x-08=0 eching

$$30 x ^ { 2 } + 2 x - 08 = 0$$

x uchun yechish

$$x=-\frac{1}{15}\approx -0,066666667$$

$$x=0$$

Faktorlash qadamlari

0 hosil qilish uchun 0 va 8 ni ko'paytirish.

$$30x^{2}+2x-0=0$$

Shartlarni qayta saralash.

$$30x^{2}+2x=0$$

x omili.

$$x\left(30x+2\right)=0$$

Tenglamani yechish uchun x=0 va 30x+2=0 ni yeching.

$$x=0 x=-\frac{1}{15}$$

Kvadrat tenglamalaridan foydalanish qoidalari

0 hosil qilish uchun 0 va 8 ni ko'paytirish.

$$30x^{2}+2x-0=0$$

Shartlarni qayta saralash.

$$30x^{2}+2x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 30 ni a, 2 ni b va 0 ni c bilan almashtiring.

$$x=\frac{-2±\sqrt{2^{2}}}{2\times 30}$$

2^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-2±2}{2\times 30}$$

2 ni 30 marotabaga ko'paytirish.

$$x=\frac{-2±2}{60}$$

x=\frac{-2±2}{60} tenglamasini yeching, bunda ± musbat. -2 ni 2 ga qo'shish.

$$x=\frac{0}{60}$$

0 ni 60 ga bo'lish.

$$x=0$$

x=\frac{-2±2}{60} tenglamasini yeching, bunda ± manfiy. -2 dan 2 ni ayirish.

$$x=-\frac{4}{60}$$

\frac{-4}{60} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=-\frac{1}{15}$$

Tenglama yechildi.

$$x=0 x=-\frac{1}{15}$$

Kvadratni yakunlash bo'yicha qadamlar

0 hosil qilish uchun 0 va 8 ni ko'paytirish.

$$30x^{2}+2x-0=0$$

0 ni ikki tarafga qo’shing.

$$30x^{2}+2x=0+0$$

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

$$30x^{2}+2x=0$$

Ikki tarafini 30 ga bo‘ling.

$$\frac{30x^{2}+2x}{30}=\frac{0}{30}$$

30 ga bo'lish 30 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{2}{30}x=\frac{0}{30}$$

\frac{2}{30} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}+\frac{1}{15}x=\frac{0}{30}$$

0 ni 30 ga bo'lish.

$$x^{2}+\frac{1}{15}x=0$$

\frac{1}{15} ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{1}{30} olish uchun. Keyin, \frac{1}{30} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+\frac{1}{15}x+\left(\frac{1}{30}\right)^{2}=\left(\frac{1}{30}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{1}{30} kvadratini chiqarish.

$$x^{2}+\frac{1}{15}x+\frac{1}{900}=\frac{1}{900}$$

x^{2}+\frac{1}{15}x+\frac{1}{900} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+\frac{1}{30}\right)^{2}=\frac{1}{900}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{1}{30}\right)^{2}}=\sqrt{\frac{1}{900}}$$

Qisqartirish.

$$x+\frac{1}{30}=\frac{1}{30} x+\frac{1}{30}=-\frac{1}{30}$$

Tenglamaning ikkala tarafidan \frac{1}{30} ni ayirish.

$$x=0 x=-\frac{1}{15}$$