1/4x-2x(x+6)=0 eching

$$\frac{ 1 }{ 4 } x-2x(x+6)=0$$

x uchun yechish

$$x = -\frac{47}{8} = -5\frac{7}{8} = -5,875$$

$$x=0$$

Faktorlash qadamlari

-2 hosil qilish uchun -1 va 2 ni ko'paytirish.

$$\frac{1}{4}x-2x\left(x+6\right)=0$$

-2x ga x+6 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{1}{4}x-2x^{2}-12x=0$$

-\frac{47}{4}x ni olish uchun \frac{1}{4}x va -12x ni birlashtirish.

$$-\frac{47}{4}x-2x^{2}=0$$

x omili.

$$x\left(-\frac{47}{4}-2x\right)=0$$

Tenglamani yechish uchun x=0 va -\frac{47}{4}-2x=0 ni yeching.

$$x=0 x=-\frac{47}{8}$$

Kvadrat tenglamalaridan foydalanish qoidalari

-2 hosil qilish uchun -1 va 2 ni ko'paytirish.

$$\frac{1}{4}x-2x\left(x+6\right)=0$$

-2x ga x+6 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{1}{4}x-2x^{2}-12x=0$$

-\frac{47}{4}x ni olish uchun \frac{1}{4}x va -12x ni birlashtirish.

$$-\frac{47}{4}x-2x^{2}=0$$

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.

$$-2x^{2}-\frac{47}{4}x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -2 ni a, -\frac{47}{4} ni b va 0 ni c bilan almashtiring.

$$x=\frac{-\left(-\frac{47}{4}\right)±\sqrt{\left(-\frac{47}{4}\right)^{2}}}{2\left(-2\right)}$$

\left(-\frac{47}{4}\right)^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-\frac{47}{4}\right)±\frac{47}{4}}{2\left(-2\right)}$$

-\frac{47}{4} ning teskarisi \frac{47}{4} ga teng.

$$x=\frac{\frac{47}{4}±\frac{47}{4}}{2\left(-2\right)}$$

2 ni -2 marotabaga ko'paytirish.

$$x=\frac{\frac{47}{4}±\frac{47}{4}}{-4}$$

x=\frac{\frac{47}{4}±\frac{47}{4}}{-4} tenglamasini yeching, bunda ± musbat. Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{47}{4} ni \frac{47}{4} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x=\frac{\frac{47}{2}}{-4}$$

\frac{47}{2} ni -4 ga bo'lish.

$$x=-\frac{47}{8}$$

x=\frac{\frac{47}{4}±\frac{47}{4}}{-4} tenglamasini yeching, bunda ± manfiy. Umumiy maxrajni topib va suratlarni ayirib \frac{47}{4} ni \frac{47}{4} dan ayirish. So'ngra imkoni boricha kasrni eng kichik shartga qisqartirish.

$$x=\frac{0}{-4}$$

0 ni -4 ga bo'lish.

$$x=0$$

Tenglama yechildi.

$$x=-\frac{47}{8} x=0$$

Kvadratni yakunlash bo'yicha qadamlar

-2 hosil qilish uchun -1 va 2 ni ko'paytirish.

$$\frac{1}{4}x-2x\left(x+6\right)=0$$

-2x ga x+6 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{1}{4}x-2x^{2}-12x=0$$

-\frac{47}{4}x ni olish uchun \frac{1}{4}x va -12x ni birlashtirish.

$$-\frac{47}{4}x-2x^{2}=0$$

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

$$-2x^{2}-\frac{47}{4}x=0$$

Ikki tarafini -2 ga bo‘ling.

$$\frac{-2x^{2}-\frac{47}{4}x}{-2}=\frac{0}{-2}$$

-2 ga bo'lish -2 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{\frac{47}{4}}{-2}\right)x=\frac{0}{-2}$$

-\frac{47}{4} ni -2 ga bo'lish.

$$x^{2}+\frac{47}{8}x=\frac{0}{-2}$$

0 ni -2 ga bo'lish.

$$x^{2}+\frac{47}{8}x=0$$

\frac{47}{8} ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{47}{16} olish uchun. Keyin, \frac{47}{16} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+\frac{47}{8}x+\left(\frac{47}{16}\right)^{2}=\left(\frac{47}{16}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{47}{16} kvadratini chiqarish.

$$x^{2}+\frac{47}{8}x+\frac{2209}{256}=\frac{2209}{256}$$

x^{2}+\frac{47}{8}x+\frac{2209}{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.

$$\left(x+\frac{47}{16}\right)^{2}=\frac{2209}{256}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{47}{16}\right)^{2}}=\sqrt{\frac{2209}{256}}$$

Qisqartirish.

$$x+\frac{47}{16}=\frac{47}{16} x+\frac{47}{16}=-\frac{47}{16}$$

Tenglamaning ikkala tarafidan \frac{47}{16} ni ayirish.

$$x=0 x=-\frac{47}{8}$$