-6/x=-x+5 eching

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

x uchun yechish

$$x=-1$$

$$x=6$$

Kvadrat tenglamalaridan foydalanish qoidalari

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

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

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

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

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

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

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.

$$x=\frac{-5±\sqrt{5^{2}-4\left(-1\right)\times 6}}{2\left(-1\right)}$$

5 kvadratini chiqarish.

$$x=\frac{-5±\sqrt{25-4\left(-1\right)\times 6}}{2\left(-1\right)}$$

-4 ni -1 marotabaga ko'paytirish.

$$x=\frac{-5±\sqrt{25+4\times 6}}{2\left(-1\right)}$$

4 ni 6 marotabaga ko'paytirish.

$$x=\frac{-5±\sqrt{25+24}}{2\left(-1\right)}$$

25 ni 24 ga qo'shish.

$$x=\frac{-5±\sqrt{49}}{2\left(-1\right)}$$

49 ning kvadrat ildizini chiqarish.

$$x=\frac{-5±7}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{-5±7}{-2}$$

x=\frac{-5±7}{-2} tenglamasini yeching, bunda ± musbat. -5 ni 7 ga qo'shish.

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

2 ni -2 ga bo'lish.

$$x=-1$$

x=\frac{-5±7}{-2} tenglamasini yeching, bunda ± manfiy. -5 dan 7 ni ayirish.

$$x=-\frac{12}{-2}$$

-12 ni -2 ga bo'lish.

$$x=6$$

Tenglama yechildi.

$$x=-1 x=6$$

Kvadratni yakunlash bo'yicha qadamlar

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

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

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

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

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

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

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

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

Ikki tarafini -1 ga bo‘ling.

$$\frac{-x^{2}+5x}{-1}=-\frac{6}{-1}$$

-1 ga bo'lish -1 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{5}{-1}x=-\frac{6}{-1}$$

5 ni -1 ga bo'lish.

$$x^{2}-5x=-\frac{6}{-1}$$

-6 ni -1 ga bo'lish.

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

-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.

$$x^{2}-5x+\frac{25}{4}=\frac{49}{4}$$

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.

$$\left(x-\frac{5}{2}\right)^{2}=\frac{49}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{5}{2}\right)^{2}}=\sqrt{\frac{49}{4}}$$

Qisqartirish.

$$x-\frac{5}{2}=\frac{7}{2} x-\frac{5}{2}=-\frac{7}{2}$$

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

$$x=6 x=-1$$