3x(2x-1)+8x=1 eching

$$3 x ( 2 x - 1 ) + 8 x = 1$$

x uchun yechish

$$x=-1$$

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

Kvadrat tenglamalaridan foydalanish qoidalari

3x ga 2x-1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$6x^{2}-3x+8x=1$$

5x ni olish uchun -3x va 8x ni birlashtirish.

$$6x^{2}+5x=1$$

Ikkala tarafdan 1 ni ayirish.

$$6x^{2}+5x-1=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 6 ni a, 5 ni b va -1 ni c bilan almashtiring.

$$x=\frac{-5±\sqrt{5^{2}-4\times 6\left(-1\right)}}{2\times 6}$$

5 kvadratini chiqarish.

$$x=\frac{-5±\sqrt{25-4\times 6\left(-1\right)}}{2\times 6}$$

-4 ni 6 marotabaga ko'paytirish.

$$x=\frac{-5±\sqrt{25-24\left(-1\right)}}{2\times 6}$$

-24 ni -1 marotabaga ko'paytirish.

$$x=\frac{-5±\sqrt{25+24}}{2\times 6}$$

25 ni 24 ga qo'shish.

$$x=\frac{-5±\sqrt{49}}{2\times 6}$$

49 ning kvadrat ildizini chiqarish.

$$x=\frac{-5±7}{2\times 6}$$

2 ni 6 marotabaga ko'paytirish.

$$x=\frac{-5±7}{12}$$

x=\frac{-5±7}{12} tenglamasini yeching, bunda ± musbat. -5 ni 7 ga qo'shish.

$$x=\frac{2}{12}$$

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

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

x=\frac{-5±7}{12} tenglamasini yeching, bunda ± manfiy. -5 dan 7 ni ayirish.

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

-12 ni 12 ga bo'lish.

$$x=-1$$

Tenglama yechildi.

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

Kvadratni yakunlash bo'yicha qadamlar

3x ga 2x-1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$6x^{2}-3x+8x=1$$

5x ni olish uchun -3x va 8x ni birlashtirish.

$$6x^{2}+5x=1$$

Ikki tarafini 6 ga bo‘ling.

$$\frac{6x^{2}+5x}{6}=\frac{1}{6}$$

6 ga bo'lish 6 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{5}{6}x=\frac{1}{6}$$

\frac{5}{6} ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{5}{12} olish uchun. Keyin, \frac{5}{12} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+\frac{5}{6}x+\left(\frac{5}{12}\right)^{2}=\frac{1}{6}+\left(\frac{5}{12}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{5}{12} kvadratini chiqarish.

$$x^{2}+\frac{5}{6}x+\frac{25}{144}=\frac{1}{6}+\frac{25}{144}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{1}{6} ni \frac{25}{144} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}+\frac{5}{6}x+\frac{25}{144}=\frac{49}{144}$$

x^{2}+\frac{5}{6}x+\frac{25}{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.

$$\left(x+\frac{5}{12}\right)^{2}=\frac{49}{144}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{5}{12}\right)^{2}}=\sqrt{\frac{49}{144}}$$

Qisqartirish.

$$x+\frac{5}{12}=\frac{7}{12} x+\frac{5}{12}=-\frac{7}{12}$$

Tenglamaning ikkala tarafidan \frac{5}{12} ni ayirish.

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