x=x+2-16/x-4 eching

$$x = \frac { x + 2 - 16 } { x - 4 }$$

x uchun yechish (complex solution)

$$x=\frac{5+\sqrt{31}i}{2}\approx 2,5+2,783882181i$$

$$x=\frac{-\sqrt{31}i+5}{2}\approx 2,5-2,783882181i$$

Kvadrat tenglamalaridan foydalanish qoidalari

-14 olish uchun 2 dan 16 ni ayirish.

$$x=\frac{x-14}{x-4}$$

Ikkala tarafdan \frac{x-14}{x-4} ni ayirish.

$$x-\frac{x-14}{x-4}=0$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x ni \frac{x-4}{x-4} marotabaga ko'paytirish.

$$\frac{x\left(x-4\right)}{x-4}-\frac{x-14}{x-4}=0$$

\frac{x\left(x-4\right)}{x-4} va \frac{x-14}{x-4} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{x\left(x-4\right)-\left(x-14\right)}{x-4}=0$$

x\left(x-4\right)-\left(x-14\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{x^{2}-4x-x+14}{x-4}=0$$

x^{2}-4x-x+14 kabi iboralarga o‘xshab birlashtiring.

$$\frac{x^{2}-5x+14}{x-4}=0$$

x qiymati 4 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x-4 ga ko'paytirish.

$$x^{2}-5x+14=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -5 ni b va 14 ni c bilan almashtiring.

$$x=\frac{-\left(-5\right)±\sqrt{\left(-5\right)^{2}-4\times 14}}{2}$$

-5 kvadratini chiqarish.

$$x=\frac{-\left(-5\right)±\sqrt{25-4\times 14}}{2}$$

-4 ni 14 marotabaga ko'paytirish.

$$x=\frac{-\left(-5\right)±\sqrt{25-56}}{2}$$

25 ni -56 ga qo'shish.

$$x=\frac{-\left(-5\right)±\sqrt{-31}}{2}$$

-31 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-5\right)±\sqrt{31}i}{2}$$

-5 ning teskarisi 5 ga teng.

$$x=\frac{5±\sqrt{31}i}{2}$$

x=\frac{5±\sqrt{31}i}{2} tenglamasini yeching, bunda ± musbat. 5 ni i\sqrt{31} ga qo'shish.

$$x=\frac{5+\sqrt{31}i}{2}$$

x=\frac{5±\sqrt{31}i}{2} tenglamasini yeching, bunda ± manfiy. 5 dan i\sqrt{31} ni ayirish.

$$x=\frac{-\sqrt{31}i+5}{2}$$

Tenglama yechildi.

$$x=\frac{5+\sqrt{31}i}{2} x=\frac{-\sqrt{31}i+5}{2}$$

Kvadratni yakunlash bo'yicha qadamlar

-14 olish uchun 2 dan 16 ni ayirish.

$$x=\frac{x-14}{x-4}$$

Ikkala tarafdan \frac{x-14}{x-4} ni ayirish.

$$x-\frac{x-14}{x-4}=0$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x ni \frac{x-4}{x-4} marotabaga ko'paytirish.

$$\frac{x\left(x-4\right)}{x-4}-\frac{x-14}{x-4}=0$$

\frac{x\left(x-4\right)}{x-4} va \frac{x-14}{x-4} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{x\left(x-4\right)-\left(x-14\right)}{x-4}=0$$

x\left(x-4\right)-\left(x-14\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{x^{2}-4x-x+14}{x-4}=0$$

x^{2}-4x-x+14 kabi iboralarga o‘xshab birlashtiring.

$$\frac{x^{2}-5x+14}{x-4}=0$$

x qiymati 4 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x-4 ga ko'paytirish.

$$x^{2}-5x+14=0$$

Ikkala tarafdan 14 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$x^{2}-5x=-14$$

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

$$x^{2}-5x+\left(-\frac{5}{2}\right)^{2}=-14+\left(-\frac{5}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{5}{2} kvadratini chiqarish.

$$x^{2}-5x+\frac{25}{4}=-14+\frac{25}{4}$$

-14 ni \frac{25}{4} ga qo'shish.

$$x^{2}-5x+\frac{25}{4}=-\frac{31}{4}$$

x^{2}-5x+\frac{25}{4} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{5}{2}\right)^{2}=-\frac{31}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{5}{2}\right)^{2}}=\sqrt{-\frac{31}{4}}$$

Qisqartirish.

$$x-\frac{5}{2}=\frac{\sqrt{31}i}{2} x-\frac{5}{2}=-\frac{\sqrt{31}i}{2}$$

\frac{5}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{5+\sqrt{31}i}{2} x=\frac{-\sqrt{31}i+5}{2}$$