x=1/x+1/6 eching

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

x uchun yechish

$$x = \frac{\sqrt{145} + 1}{12} \approx 1,086799548$$

$$x=\frac{1-\sqrt{145}}{12}\approx -0,920132882$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x va 6 ning eng kichik umumiy karralisi 6x. \frac{1}{x} ni \frac{6}{6} marotabaga ko'paytirish. \frac{1}{6} ni \frac{x}{x} marotabaga ko'paytirish.

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

\frac{6}{6x} va \frac{x}{6x} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

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

Ikkala tarafdan \frac{6+x}{6x} ni ayirish.

$$x-\frac{6+x}{6x}=0$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x ni \frac{6x}{6x} marotabaga ko'paytirish.

$$\frac{x\times 6x}{6x}-\frac{6+x}{6x}=0$$

\frac{x\times 6x}{6x} va \frac{6+x}{6x} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

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

x\times 6x-\left(6+x\right) ichidagi ko‘paytirishlarni bajaring.

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

\frac{6x^{2}-6-x}{6x} ichida hali faktorlanmagan ifodalarni faktorlang.

$$\frac{6\left(x-\left(-\frac{1}{12}\sqrt{145}+\frac{1}{12}\right)\right)\left(x-\left(\frac{1}{12}\sqrt{145}+\frac{1}{12}\right)\right)}{6x}=0$$

Surat va maxrajdagi ikkala 6 ni qisqartiring.

$$\frac{\left(x-\left(-\frac{1}{12}\sqrt{145}+\frac{1}{12}\right)\right)\left(x-\left(\frac{1}{12}\sqrt{145}+\frac{1}{12}\right)\right)}{x}=0$$

x qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x ga ko'paytirish.

$$\left(x-\left(-\frac{1}{12}\sqrt{145}+\frac{1}{12}\right)\right)\left(x-\left(\frac{1}{12}\sqrt{145}+\frac{1}{12}\right)\right)=0$$

-\frac{1}{12}\sqrt{145}+\frac{1}{12} teskarisini topish uchun har birining teskarisini toping.

$$\left(x-\left(-\frac{1}{12}\sqrt{145}\right)-\frac{1}{12}\right)\left(x-\left(\frac{1}{12}\sqrt{145}+\frac{1}{12}\right)\right)=0$$

-\frac{1}{12}\sqrt{145} ning teskarisi \frac{1}{12}\sqrt{145} ga teng.

$$\left(x+\frac{1}{12}\sqrt{145}-\frac{1}{12}\right)\left(x-\left(\frac{1}{12}\sqrt{145}+\frac{1}{12}\right)\right)=0$$

\frac{1}{12}\sqrt{145}+\frac{1}{12} teskarisini topish uchun har birining teskarisini toping.

$$\left(x+\frac{1}{12}\sqrt{145}-\frac{1}{12}\right)\left(x-\frac{1}{12}\sqrt{145}-\frac{1}{12}\right)=0$$

x+\frac{1}{12}\sqrt{145}-\frac{1}{12} ifodaning har bir elementini x-\frac{1}{12}\sqrt{145}-\frac{1}{12} ifodaning har bir elementiga ko‘paytirish orqali taqsimot qonuni xususiyatlarini qo‘llash mumkin.

$$x^{2}+x\left(-\frac{1}{12}\right)\sqrt{145}+x\left(-\frac{1}{12}\right)+\frac{1}{12}\sqrt{145}x+\frac{1}{12}\sqrt{145}\left(-\frac{1}{12}\right)\sqrt{145}+\frac{1}{12}\sqrt{145}\left(-\frac{1}{12}\right)-\frac{1}{12}x-\frac{1}{12}\left(-\frac{1}{12}\right)\sqrt{145}-\frac{1}{12}\left(-\frac{1}{12}\right)=0$$

145 hosil qilish uchun \sqrt{145} va \sqrt{145} ni ko'paytirish.

$$x^{2}+x\left(-\frac{1}{12}\right)\sqrt{145}+x\left(-\frac{1}{12}\right)+\frac{1}{12}\sqrt{145}x+\frac{1}{12}\times 145\left(-\frac{1}{12}\right)+\frac{1}{12}\sqrt{145}\left(-\frac{1}{12}\right)-\frac{1}{12}x-\frac{1}{12}\left(-\frac{1}{12}\right)\sqrt{145}-\frac{1}{12}\left(-\frac{1}{12}\right)=0$$

0 ni olish uchun x\left(-\frac{1}{12}\right)\sqrt{145} va \frac{1}{12}\sqrt{145}x ni birlashtirish.

$$x^{2}+x\left(-\frac{1}{12}\right)+\frac{1}{12}\times 145\left(-\frac{1}{12}\right)+\frac{1}{12}\sqrt{145}\left(-\frac{1}{12}\right)-\frac{1}{12}x-\frac{1}{12}\left(-\frac{1}{12}\right)\sqrt{145}-\frac{1}{12}\left(-\frac{1}{12}\right)=0$$

\frac{145}{12} hosil qilish uchun \frac{1}{12} va 145 ni ko'paytirish.

$$x^{2}+x\left(-\frac{1}{12}\right)+\frac{145}{12}\left(-\frac{1}{12}\right)+\frac{1}{12}\sqrt{145}\left(-\frac{1}{12}\right)-\frac{1}{12}x-\frac{1}{12}\left(-\frac{1}{12}\right)\sqrt{145}-\frac{1}{12}\left(-\frac{1}{12}\right)=0$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{145}{12} ni -\frac{1}{12} ga ko‘paytiring.

$$x^{2}+x\left(-\frac{1}{12}\right)+\frac{145\left(-1\right)}{12\times 12}+\frac{1}{12}\sqrt{145}\left(-\frac{1}{12}\right)-\frac{1}{12}x-\frac{1}{12}\left(-\frac{1}{12}\right)\sqrt{145}-\frac{1}{12}\left(-\frac{1}{12}\right)=0$$

\frac{145\left(-1\right)}{12\times 12} kasridagi ko‘paytirishlarni bajaring.

$$x^{2}+x\left(-\frac{1}{12}\right)+\frac{-145}{144}+\frac{1}{12}\sqrt{145}\left(-\frac{1}{12}\right)-\frac{1}{12}x-\frac{1}{12}\left(-\frac{1}{12}\right)\sqrt{145}-\frac{1}{12}\left(-\frac{1}{12}\right)=0$$

\frac{-145}{144} kasri manfiy belgini olib tashlash bilan -\frac{145}{144} sifatida qayta yozilishi mumkin.

$$x^{2}+x\left(-\frac{1}{12}\right)-\frac{145}{144}+\frac{1}{12}\sqrt{145}\left(-\frac{1}{12}\right)-\frac{1}{12}x-\frac{1}{12}\left(-\frac{1}{12}\right)\sqrt{145}-\frac{1}{12}\left(-\frac{1}{12}\right)=0$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{1}{12} ni -\frac{1}{12} ga ko‘paytiring.

$$x^{2}+x\left(-\frac{1}{12}\right)-\frac{145}{144}+\frac{1\left(-1\right)}{12\times 12}\sqrt{145}-\frac{1}{12}x-\frac{1}{12}\left(-\frac{1}{12}\right)\sqrt{145}-\frac{1}{12}\left(-\frac{1}{12}\right)=0$$

\frac{1\left(-1\right)}{12\times 12} kasridagi ko‘paytirishlarni bajaring.

$$x^{2}+x\left(-\frac{1}{12}\right)-\frac{145}{144}+\frac{-1}{144}\sqrt{145}-\frac{1}{12}x-\frac{1}{12}\left(-\frac{1}{12}\right)\sqrt{145}-\frac{1}{12}\left(-\frac{1}{12}\right)=0$$

\frac{-1}{144} kasri manfiy belgini olib tashlash bilan -\frac{1}{144} sifatida qayta yozilishi mumkin.

$$x^{2}+x\left(-\frac{1}{12}\right)-\frac{145}{144}-\frac{1}{144}\sqrt{145}-\frac{1}{12}x-\frac{1}{12}\left(-\frac{1}{12}\right)\sqrt{145}-\frac{1}{12}\left(-\frac{1}{12}\right)=0$$

-\frac{1}{6}x ni olish uchun x\left(-\frac{1}{12}\right) va -\frac{1}{12}x ni birlashtirish.

$$x^{2}-\frac{1}{6}x-\frac{145}{144}-\frac{1}{144}\sqrt{145}-\frac{1}{12}\left(-\frac{1}{12}\right)\sqrt{145}-\frac{1}{12}\left(-\frac{1}{12}\right)=0$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali -\frac{1}{12} ni -\frac{1}{12} ga ko‘paytiring.

$$x^{2}-\frac{1}{6}x-\frac{145}{144}-\frac{1}{144}\sqrt{145}+\frac{-\left(-1\right)}{12\times 12}\sqrt{145}-\frac{1}{12}\left(-\frac{1}{12}\right)=0$$

\frac{-\left(-1\right)}{12\times 12} kasridagi ko‘paytirishlarni bajaring.

$$x^{2}-\frac{1}{6}x-\frac{145}{144}-\frac{1}{144}\sqrt{145}+\frac{1}{144}\sqrt{145}-\frac{1}{12}\left(-\frac{1}{12}\right)=0$$

0 ni olish uchun -\frac{1}{144}\sqrt{145} va \frac{1}{144}\sqrt{145} ni birlashtirish.

$$x^{2}-\frac{1}{6}x-\frac{145}{144}-\frac{1}{12}\left(-\frac{1}{12}\right)=0$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali -\frac{1}{12} ni -\frac{1}{12} ga ko‘paytiring.

$$x^{2}-\frac{1}{6}x-\frac{145}{144}+\frac{-\left(-1\right)}{12\times 12}=0$$

\frac{-\left(-1\right)}{12\times 12} kasridagi ko‘paytirishlarni bajaring.

$$x^{2}-\frac{1}{6}x-\frac{145}{144}+\frac{1}{144}=0$$

-\frac{145}{144} va \frac{1}{144} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$x^{2}-\frac{1}{6}x+\frac{-145+1}{144}=0$$

-144 olish uchun -145 va 1'ni qo'shing.

$$x^{2}-\frac{1}{6}x+\frac{-144}{144}=0$$

-1 ni olish uchun -144 ni 144 ga bo‘ling.

$$x^{2}-\frac{1}{6}x-1=0$$

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

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

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

$$x=\frac{-\left(-\frac{1}{6}\right)±\sqrt{\frac{1}{36}-4\left(-1\right)}}{2}$$

-4 ni -1 marotabaga ko'paytirish.

$$x=\frac{-\left(-\frac{1}{6}\right)±\sqrt{\frac{1}{36}+4}}{2}$$

\frac{1}{36} ni 4 ga qo'shish.

$$x=\frac{-\left(-\frac{1}{6}\right)±\sqrt{\frac{145}{36}}}{2}$$

\frac{145}{36} ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-\frac{1}{6}\right)±\frac{\sqrt{145}}{6}}{2}$$

-\frac{1}{6} ning teskarisi \frac{1}{6} ga teng.

$$x=\frac{\frac{1}{6}±\frac{\sqrt{145}}{6}}{2}$$

x=\frac{\frac{1}{6}±\frac{\sqrt{145}}{6}}{2} tenglamasini yeching, bunda ± musbat. \frac{1}{6} ni \frac{\sqrt{145}}{6} ga qo'shish.

$$x=\frac{\sqrt{145}+1}{2\times 6}$$

\frac{1+\sqrt{145}}{6} ni 2 ga bo'lish.

$$x=\frac{\sqrt{145}+1}{12}$$

x=\frac{\frac{1}{6}±\frac{\sqrt{145}}{6}}{2} tenglamasini yeching, bunda ± manfiy. \frac{1}{6} dan \frac{\sqrt{145}}{6} ni ayirish.

$$x=\frac{1-\sqrt{145}}{2\times 6}$$

\frac{1-\sqrt{145}}{6} ni 2 ga bo'lish.

$$x=\frac{1-\sqrt{145}}{12}$$

Tenglama yechildi.

$$x=\frac{\sqrt{145}+1}{12} x=\frac{1-\sqrt{145}}{12}$$

Kvadratni yakunlash bo'yicha qadamlar

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x va 6 ning eng kichik umumiy karralisi 6x. \frac{1}{x} ni \frac{6}{6} marotabaga ko'paytirish. \frac{1}{6} ni \frac{x}{x} marotabaga ko'paytirish.

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

\frac{6}{6x} va \frac{x}{6x} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

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

Ikkala tarafdan \frac{6+x}{6x} ni ayirish.

$$x-\frac{6+x}{6x}=0$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x ni \frac{6x}{6x} marotabaga ko'paytirish.

$$\frac{x\times 6x}{6x}-\frac{6+x}{6x}=0$$

\frac{x\times 6x}{6x} va \frac{6+x}{6x} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

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

x\times 6x-\left(6+x\right) ichidagi ko‘paytirishlarni bajaring.

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

\frac{6x^{2}-6-x}{6x} ichida hali faktorlanmagan ifodalarni faktorlang.

$$\frac{6\left(x-\left(-\frac{1}{12}\sqrt{145}+\frac{1}{12}\right)\right)\left(x-\left(\frac{1}{12}\sqrt{145}+\frac{1}{12}\right)\right)}{6x}=0$$

Surat va maxrajdagi ikkala 6 ni qisqartiring.

$$\frac{\left(x-\left(-\frac{1}{12}\sqrt{145}+\frac{1}{12}\right)\right)\left(x-\left(\frac{1}{12}\sqrt{145}+\frac{1}{12}\right)\right)}{x}=0$$

x qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x ga ko'paytirish.

$$\left(x-\left(-\frac{1}{12}\sqrt{145}+\frac{1}{12}\right)\right)\left(x-\left(\frac{1}{12}\sqrt{145}+\frac{1}{12}\right)\right)=0$$

-\frac{1}{12}\sqrt{145}+\frac{1}{12} teskarisini topish uchun har birining teskarisini toping.

$$\left(x-\left(-\frac{1}{12}\sqrt{145}\right)-\frac{1}{12}\right)\left(x-\left(\frac{1}{12}\sqrt{145}+\frac{1}{12}\right)\right)=0$$

-\frac{1}{12}\sqrt{145} ning teskarisi \frac{1}{12}\sqrt{145} ga teng.

$$\left(x+\frac{1}{12}\sqrt{145}-\frac{1}{12}\right)\left(x-\left(\frac{1}{12}\sqrt{145}+\frac{1}{12}\right)\right)=0$$

\frac{1}{12}\sqrt{145}+\frac{1}{12} teskarisini topish uchun har birining teskarisini toping.

$$\left(x+\frac{1}{12}\sqrt{145}-\frac{1}{12}\right)\left(x-\frac{1}{12}\sqrt{145}-\frac{1}{12}\right)=0$$

x+\frac{1}{12}\sqrt{145}-\frac{1}{12} ifodaning har bir elementini x-\frac{1}{12}\sqrt{145}-\frac{1}{12} ifodaning har bir elementiga ko‘paytirish orqali taqsimot qonuni xususiyatlarini qo‘llash mumkin.

$$x^{2}+x\left(-\frac{1}{12}\right)\sqrt{145}+x\left(-\frac{1}{12}\right)+\frac{1}{12}\sqrt{145}x+\frac{1}{12}\sqrt{145}\left(-\frac{1}{12}\right)\sqrt{145}+\frac{1}{12}\sqrt{145}\left(-\frac{1}{12}\right)-\frac{1}{12}x-\frac{1}{12}\left(-\frac{1}{12}\right)\sqrt{145}-\frac{1}{12}\left(-\frac{1}{12}\right)=0$$

145 hosil qilish uchun \sqrt{145} va \sqrt{145} ni ko'paytirish.

$$x^{2}+x\left(-\frac{1}{12}\right)\sqrt{145}+x\left(-\frac{1}{12}\right)+\frac{1}{12}\sqrt{145}x+\frac{1}{12}\times 145\left(-\frac{1}{12}\right)+\frac{1}{12}\sqrt{145}\left(-\frac{1}{12}\right)-\frac{1}{12}x-\frac{1}{12}\left(-\frac{1}{12}\right)\sqrt{145}-\frac{1}{12}\left(-\frac{1}{12}\right)=0$$

0 ni olish uchun x\left(-\frac{1}{12}\right)\sqrt{145} va \frac{1}{12}\sqrt{145}x ni birlashtirish.

$$x^{2}+x\left(-\frac{1}{12}\right)+\frac{1}{12}\times 145\left(-\frac{1}{12}\right)+\frac{1}{12}\sqrt{145}\left(-\frac{1}{12}\right)-\frac{1}{12}x-\frac{1}{12}\left(-\frac{1}{12}\right)\sqrt{145}-\frac{1}{12}\left(-\frac{1}{12}\right)=0$$

\frac{145}{12} hosil qilish uchun \frac{1}{12} va 145 ni ko'paytirish.

$$x^{2}+x\left(-\frac{1}{12}\right)+\frac{145}{12}\left(-\frac{1}{12}\right)+\frac{1}{12}\sqrt{145}\left(-\frac{1}{12}\right)-\frac{1}{12}x-\frac{1}{12}\left(-\frac{1}{12}\right)\sqrt{145}-\frac{1}{12}\left(-\frac{1}{12}\right)=0$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{145}{12} ni -\frac{1}{12} ga ko‘paytiring.

$$x^{2}+x\left(-\frac{1}{12}\right)+\frac{145\left(-1\right)}{12\times 12}+\frac{1}{12}\sqrt{145}\left(-\frac{1}{12}\right)-\frac{1}{12}x-\frac{1}{12}\left(-\frac{1}{12}\right)\sqrt{145}-\frac{1}{12}\left(-\frac{1}{12}\right)=0$$

\frac{145\left(-1\right)}{12\times 12} kasridagi ko‘paytirishlarni bajaring.

$$x^{2}+x\left(-\frac{1}{12}\right)+\frac{-145}{144}+\frac{1}{12}\sqrt{145}\left(-\frac{1}{12}\right)-\frac{1}{12}x-\frac{1}{12}\left(-\frac{1}{12}\right)\sqrt{145}-\frac{1}{12}\left(-\frac{1}{12}\right)=0$$

\frac{-145}{144} kasri manfiy belgini olib tashlash bilan -\frac{145}{144} sifatida qayta yozilishi mumkin.

$$x^{2}+x\left(-\frac{1}{12}\right)-\frac{145}{144}+\frac{1}{12}\sqrt{145}\left(-\frac{1}{12}\right)-\frac{1}{12}x-\frac{1}{12}\left(-\frac{1}{12}\right)\sqrt{145}-\frac{1}{12}\left(-\frac{1}{12}\right)=0$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{1}{12} ni -\frac{1}{12} ga ko‘paytiring.

$$x^{2}+x\left(-\frac{1}{12}\right)-\frac{145}{144}+\frac{1\left(-1\right)}{12\times 12}\sqrt{145}-\frac{1}{12}x-\frac{1}{12}\left(-\frac{1}{12}\right)\sqrt{145}-\frac{1}{12}\left(-\frac{1}{12}\right)=0$$

\frac{1\left(-1\right)}{12\times 12} kasridagi ko‘paytirishlarni bajaring.

$$x^{2}+x\left(-\frac{1}{12}\right)-\frac{145}{144}+\frac{-1}{144}\sqrt{145}-\frac{1}{12}x-\frac{1}{12}\left(-\frac{1}{12}\right)\sqrt{145}-\frac{1}{12}\left(-\frac{1}{12}\right)=0$$

\frac{-1}{144} kasri manfiy belgini olib tashlash bilan -\frac{1}{144} sifatida qayta yozilishi mumkin.

$$x^{2}+x\left(-\frac{1}{12}\right)-\frac{145}{144}-\frac{1}{144}\sqrt{145}-\frac{1}{12}x-\frac{1}{12}\left(-\frac{1}{12}\right)\sqrt{145}-\frac{1}{12}\left(-\frac{1}{12}\right)=0$$

-\frac{1}{6}x ni olish uchun x\left(-\frac{1}{12}\right) va -\frac{1}{12}x ni birlashtirish.

$$x^{2}-\frac{1}{6}x-\frac{145}{144}-\frac{1}{144}\sqrt{145}-\frac{1}{12}\left(-\frac{1}{12}\right)\sqrt{145}-\frac{1}{12}\left(-\frac{1}{12}\right)=0$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali -\frac{1}{12} ni -\frac{1}{12} ga ko‘paytiring.

$$x^{2}-\frac{1}{6}x-\frac{145}{144}-\frac{1}{144}\sqrt{145}+\frac{-\left(-1\right)}{12\times 12}\sqrt{145}-\frac{1}{12}\left(-\frac{1}{12}\right)=0$$

\frac{-\left(-1\right)}{12\times 12} kasridagi ko‘paytirishlarni bajaring.

$$x^{2}-\frac{1}{6}x-\frac{145}{144}-\frac{1}{144}\sqrt{145}+\frac{1}{144}\sqrt{145}-\frac{1}{12}\left(-\frac{1}{12}\right)=0$$

0 ni olish uchun -\frac{1}{144}\sqrt{145} va \frac{1}{144}\sqrt{145} ni birlashtirish.

$$x^{2}-\frac{1}{6}x-\frac{145}{144}-\frac{1}{12}\left(-\frac{1}{12}\right)=0$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali -\frac{1}{12} ni -\frac{1}{12} ga ko‘paytiring.

$$x^{2}-\frac{1}{6}x-\frac{145}{144}+\frac{-\left(-1\right)}{12\times 12}=0$$

\frac{-\left(-1\right)}{12\times 12} kasridagi ko‘paytirishlarni bajaring.

$$x^{2}-\frac{1}{6}x-\frac{145}{144}+\frac{1}{144}=0$$

-\frac{145}{144} va \frac{1}{144} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$x^{2}-\frac{1}{6}x+\frac{-145+1}{144}=0$$

-144 olish uchun -145 va 1'ni qo'shing.

$$x^{2}-\frac{1}{6}x+\frac{-144}{144}=0$$

-1 ni olish uchun -144 ni 144 ga bo‘ling.

$$x^{2}-\frac{1}{6}x-1=0$$

1 ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$x^{2}-\frac{1}{6}x=1$$

-\frac{1}{6} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{1}{12} olish uchun. Keyin, -\frac{1}{12} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

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

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{1}{12} kvadratini chiqarish.

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

1 ni \frac{1}{144} ga qo'shish.

$$x^{2}-\frac{1}{6}x+\frac{1}{144}=\frac{145}{144}$$

x^{2}-\frac{1}{6}x+\frac{1}{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.

$$\left(x-\frac{1}{12}\right)^{2}=\frac{145}{144}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{1}{12}\right)^{2}}=\sqrt{\frac{145}{144}}$$

Qisqartirish.

$$x-\frac{1}{12}=\frac{\sqrt{145}}{12} x-\frac{1}{12}=-\frac{\sqrt{145}}{12}$$

\frac{1}{12} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{\sqrt{145}+1}{12} x=\frac{1-\sqrt{145}}{12}$$