-1/3x+2=-x^2+7/2x+2 eching

$$- \frac { 1 } { 3 } x + 2 = - x ^ { 2 } + \frac { 7 } { 2 } x + 2$$

x uchun yechish

$$x = \frac{23}{6} = 3\frac{5}{6} \approx 3,833333333$$

$$x=0$$

Faktorlash qadamlari

x^{2} ni ikki tarafga qo’shing.

$$-\frac{1}{3}x+2+x^{2}=\frac{7}{2}x+2$$

Ikkala tarafdan \frac{7}{2}x ni ayirish.

$$-\frac{1}{3}x+2+x^{2}-\frac{7}{2}x=2$$

-\frac{23}{6}x ni olish uchun -\frac{1}{3}x va -\frac{7}{2}x ni birlashtirish.

$$-\frac{23}{6}x+2+x^{2}=2$$

Ikkala tarafdan 2 ni ayirish.

$$-\frac{23}{6}x+2+x^{2}-2=0$$

0 olish uchun 2 dan 2 ni ayirish.

$$-\frac{23}{6}x+x^{2}=0$$

x omili.

$$x\left(-\frac{23}{6}+x\right)=0$$

Tenglamani yechish uchun x=0 va -\frac{23}{6}+x=0 ni yeching.

$$x=0 x=\frac{23}{6}$$

Kvadrat tenglamalaridan foydalanish qoidalari

x^{2} ni ikki tarafga qo’shing.

$$-\frac{1}{3}x+2+x^{2}=\frac{7}{2}x+2$$

Ikkala tarafdan \frac{7}{2}x ni ayirish.

$$-\frac{1}{3}x+2+x^{2}-\frac{7}{2}x=2$$

-\frac{23}{6}x ni olish uchun -\frac{1}{3}x va -\frac{7}{2}x ni birlashtirish.

$$-\frac{23}{6}x+2+x^{2}=2$$

Ikkala tarafdan 2 ni ayirish.

$$-\frac{23}{6}x+2+x^{2}-2=0$$

0 olish uchun 2 dan 2 ni ayirish.

$$-\frac{23}{6}x+x^{2}=0$$

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.

$$x^{2}-\frac{23}{6}x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -\frac{23}{6} ni b va 0 ni c bilan almashtiring.

$$x=\frac{-\left(-\frac{23}{6}\right)±\sqrt{\left(-\frac{23}{6}\right)^{2}}}{2}$$

\left(-\frac{23}{6}\right)^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-\frac{23}{6}\right)±\frac{23}{6}}{2}$$

-\frac{23}{6} ning teskarisi \frac{23}{6} ga teng.

$$x=\frac{\frac{23}{6}±\frac{23}{6}}{2}$$

x=\frac{\frac{23}{6}±\frac{23}{6}}{2} tenglamasini yeching, bunda ± musbat. Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{23}{6} ni \frac{23}{6} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x=\frac{\frac{23}{3}}{2}$$

\frac{23}{3} ni 2 ga bo'lish.

$$x=\frac{23}{6}$$

x=\frac{\frac{23}{6}±\frac{23}{6}}{2} tenglamasini yeching, bunda ± manfiy. Umumiy maxrajni topib va suratlarni ayirib \frac{23}{6} ni \frac{23}{6} dan ayirish. So'ngra imkoni boricha kasrni eng kichik shartga qisqartirish.

$$x=\frac{0}{2}$$

0 ni 2 ga bo'lish.

$$x=0$$

Tenglama yechildi.

$$x=\frac{23}{6} x=0$$

Kvadratni yakunlash bo'yicha qadamlar

x^{2} ni ikki tarafga qo’shing.

$$-\frac{1}{3}x+2+x^{2}=\frac{7}{2}x+2$$

Ikkala tarafdan \frac{7}{2}x ni ayirish.

$$-\frac{1}{3}x+2+x^{2}-\frac{7}{2}x=2$$

-\frac{23}{6}x ni olish uchun -\frac{1}{3}x va -\frac{7}{2}x ni birlashtirish.

$$-\frac{23}{6}x+2+x^{2}=2$$

Ikkala tarafdan 2 ni ayirish.

$$-\frac{23}{6}x+2+x^{2}-2=0$$

0 olish uchun 2 dan 2 ni ayirish.

$$-\frac{23}{6}x+x^{2}=0$$

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

$$x^{2}-\frac{23}{6}x=0$$

-\frac{23}{6} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{23}{12} olish uchun. Keyin, -\frac{23}{12} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{23}{6}x+\left(-\frac{23}{12}\right)^{2}=\left(-\frac{23}{12}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{23}{12} kvadratini chiqarish.

$$x^{2}-\frac{23}{6}x+\frac{529}{144}=\frac{529}{144}$$

x^{2}-\frac{23}{6}x+\frac{529}{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.

$$\left(x-\frac{23}{12}\right)^{2}=\frac{529}{144}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{23}{12}\right)^{2}}=\sqrt{\frac{529}{144}}$$

Qisqartirish.

$$x-\frac{23}{12}=\frac{23}{12} x-\frac{23}{12}=-\frac{23}{12}$$

\frac{23}{12} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{23}{6} x=0$$