x+5=-6/x eching

$$x + 5 = - \frac { 6 } { x }$$

x uchun yechish

$$x=-3$$

$$x=-2$$

Kvadrat tenglamalaridan foydalanish qoidalari

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

$$xx+x\times 5=-6$$

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$x^{2}+x\times 5=-6$$

6 ni ikki tarafga qo’shing.

$$x^{2}+x\times 5+6=0$$

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.

$$x^{2}+5x+6=0$$

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 6 ni c bilan almashtiring.

$$x=\frac{-5±\sqrt{5^{2}-4\times 6}}{2}$$

5 kvadratini chiqarish.

$$x=\frac{-5±\sqrt{25-4\times 6}}{2}$$

-4 ni 6 marotabaga ko'paytirish.

$$x=\frac{-5±\sqrt{25-24}}{2}$$

25 ni -24 ga qo'shish.

$$x=\frac{-5±\sqrt{1}}{2}$$

1 ning kvadrat ildizini chiqarish.

$$x=\frac{-5±1}{2}$$

x=\frac{-5±1}{2} tenglamasini yeching, bunda ± musbat. -5 ni 1 ga qo'shish.

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

-4 ni 2 ga bo'lish.

$$x=-2$$

x=\frac{-5±1}{2} tenglamasini yeching, bunda ± manfiy. -5 dan 1 ni ayirish.

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

-6 ni 2 ga bo'lish.

$$x=-3$$

Tenglama yechildi.

$$x=-2 x=-3$$

Kvadratni yakunlash bo'yicha qadamlar

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

$$xx+x\times 5=-6$$

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$x^{2}+x\times 5=-6$$

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

$$x^{2}+5x=-6$$

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.

$$x^{2}+5x+\left(\frac{5}{2}\right)^{2}=-6+\left(\frac{5}{2}\right)^{2}$$

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

$$x^{2}+5x+\frac{25}{4}=-6+\frac{25}{4}$$

-6 ni \frac{25}{4} ga qo'shish.

$$x^{2}+5x+\frac{25}{4}=\frac{1}{4}$$

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.

$$\left(x+\frac{5}{2}\right)^{2}=\frac{1}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{5}{2}\right)^{2}}=\sqrt{\frac{1}{4}}$$

Qisqartirish.

$$x+\frac{5}{2}=\frac{1}{2} x+\frac{5}{2}=-\frac{1}{2}$$

Tenglamaning ikkala tarafidan \frac{5}{2} ni ayirish.

$$x=-2 x=-3$$