4-x^2-x^2-2/3x=4 eching

$$4- { x }^{ 2 } - { x }^{ 2 } - \frac{ 2 }{ 3 } x=4$$

x uchun yechish

$$x=-\frac{1}{3}\approx -0,333333333$$

$$x=0$$

Faktorlash qadamlari

-2x^{2} ni olish uchun -x^{2} va -x^{2} ni birlashtirish.

$$4-2x^{2}-\frac{2}{3}x=4$$

Ikkala tarafdan 4 ni ayirish.

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

0 olish uchun 4 dan 4 ni ayirish.

$$-2x^{2}-\frac{2}{3}x=0$$

x omili.

$$x\left(-2x-\frac{2}{3}\right)=0$$

Tenglamani yechish uchun x=0 va -2x-\frac{2}{3}=0 ni yeching.

$$x=0 x=-\frac{1}{3}$$

Kvadrat tenglamalaridan foydalanish qoidalari

-2x^{2} ni olish uchun -x^{2} va -x^{2} ni birlashtirish.

$$4-2x^{2}-\frac{2}{3}x=4$$

Ikkala tarafdan 4 ni ayirish.

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

0 olish uchun 4 dan 4 ni ayirish.

$$-2x^{2}-\frac{2}{3}x=0$$

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

$$x=\frac{-\left(-\frac{2}{3}\right)±\sqrt{\left(-\frac{2}{3}\right)^{2}}}{2\left(-2\right)}$$

\left(-\frac{2}{3}\right)^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-\frac{2}{3}\right)±\frac{2}{3}}{2\left(-2\right)}$$

-\frac{2}{3} ning teskarisi \frac{2}{3} ga teng.

$$x=\frac{\frac{2}{3}±\frac{2}{3}}{2\left(-2\right)}$$

2 ni -2 marotabaga ko'paytirish.

$$x=\frac{\frac{2}{3}±\frac{2}{3}}{-4}$$

x=\frac{\frac{2}{3}±\frac{2}{3}}{-4} tenglamasini yeching, bunda ± musbat. Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{2}{3} ni \frac{2}{3} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x=\frac{\frac{4}{3}}{-4}$$

\frac{4}{3} ni -4 ga bo'lish.

$$x=-\frac{1}{3}$$

x=\frac{\frac{2}{3}±\frac{2}{3}}{-4} tenglamasini yeching, bunda ± manfiy. Umumiy maxrajni topib va suratlarni ayirib \frac{2}{3} ni \frac{2}{3} 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.

$$x=-\frac{1}{3} x=0$$

Kvadratni yakunlash bo'yicha qadamlar

-2x^{2} ni olish uchun -x^{2} va -x^{2} ni birlashtirish.

$$4-2x^{2}-\frac{2}{3}x=4$$

Ikkala tarafdan 4 ni ayirish.

$$-2x^{2}-\frac{2}{3}x=4-4$$

0 olish uchun 4 dan 4 ni ayirish.

$$-2x^{2}-\frac{2}{3}x=0$$

Ikki tarafini -2 ga bo‘ling.

$$\frac{-2x^{2}-\frac{2}{3}x}{-2}=\frac{0}{-2}$$

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

$$x^{2}+\left(-\frac{\frac{2}{3}}{-2}\right)x=\frac{0}{-2}$$

-\frac{2}{3} ni -2 ga bo'lish.

$$x^{2}+\frac{1}{3}x=\frac{0}{-2}$$

0 ni -2 ga bo'lish.

$$x^{2}+\frac{1}{3}x=0$$

\frac{1}{3} ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{1}{6} olish uchun. Keyin, \frac{1}{6} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+\frac{1}{3}x+\left(\frac{1}{6}\right)^{2}=\left(\frac{1}{6}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{1}{6} kvadratini chiqarish.

$$x^{2}+\frac{1}{3}x+\frac{1}{36}=\frac{1}{36}$$

x^{2}+\frac{1}{3}x+\frac{1}{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.

$$\left(x+\frac{1}{6}\right)^{2}=\frac{1}{36}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{1}{6}\right)^{2}}=\sqrt{\frac{1}{36}}$$

Qisqartirish.

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

Tenglamaning ikkala tarafidan \frac{1}{6} ni ayirish.

$$x=0 x=-\frac{1}{3}$$