7+x/10=2/x+6 eching

$$\frac{ 7+x }{ 10 } = \frac{ 2 }{ x+6 }$$

x uchun yechish

$$x=-11$$

$$x=-2$$

Kvadrat tenglamalaridan foydalanish qoidalari

x qiymati -6 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 10\left(x+6\right) ga, 10,x+6 ning eng kichik karralisiga ko‘paytiring.

$$\left(x+6\right)\left(7+x\right)=10\times 2$$

x+6 ga 7+x ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$13x+x^{2}+42=10\times 2$$

20 hosil qilish uchun 10 va 2 ni ko'paytirish.

$$13x+x^{2}+42=20$$

Ikkala tarafdan 20 ni ayirish.

$$13x+x^{2}+42-20=0$$

22 olish uchun 42 dan 20 ni ayirish.

$$13x+x^{2}+22=0$$

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.

$$x^{2}+13x+22=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 13 ni b va 22 ni c bilan almashtiring.

$$x=\frac{-13±\sqrt{13^{2}-4\times 22}}{2}$$

13 kvadratini chiqarish.

$$x=\frac{-13±\sqrt{169-4\times 22}}{2}$$

-4 ni 22 marotabaga ko'paytirish.

$$x=\frac{-13±\sqrt{169-88}}{2}$$

169 ni -88 ga qo'shish.

$$x=\frac{-13±\sqrt{81}}{2}$$

81 ning kvadrat ildizini chiqarish.

$$x=\frac{-13±9}{2}$$

x=\frac{-13±9}{2} tenglamasini yeching, bunda ± musbat. -13 ni 9 ga qo'shish.

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

-4 ni 2 ga bo'lish.

$$x=-2$$

x=\frac{-13±9}{2} tenglamasini yeching, bunda ± manfiy. -13 dan 9 ni ayirish.

$$x=-\frac{22}{2}$$

-22 ni 2 ga bo'lish.

$$x=-11$$

Tenglama yechildi.

$$x=-2 x=-11$$

Kvadratni yakunlash bo'yicha qadamlar

x qiymati -6 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 10\left(x+6\right) ga, 10,x+6 ning eng kichik karralisiga ko‘paytiring.

$$\left(x+6\right)\left(7+x\right)=10\times 2$$

x+6 ga 7+x ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$13x+x^{2}+42=10\times 2$$

20 hosil qilish uchun 10 va 2 ni ko'paytirish.

$$13x+x^{2}+42=20$$

Ikkala tarafdan 42 ni ayirish.

$$13x+x^{2}=20-42$$

-22 olish uchun 20 dan 42 ni ayirish.

$$13x+x^{2}=-22$$

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

$$x^{2}+13x=-22$$

13 ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{13}{2} olish uchun. Keyin, \frac{13}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+13x+\left(\frac{13}{2}\right)^{2}=-22+\left(\frac{13}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{13}{2} kvadratini chiqarish.

$$x^{2}+13x+\frac{169}{4}=-22+\frac{169}{4}$$

-22 ni \frac{169}{4} ga qo'shish.

$$x^{2}+13x+\frac{169}{4}=\frac{81}{4}$$

x^{2}+13x+\frac{169}{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.

$$\left(x+\frac{13}{2}\right)^{2}=\frac{81}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{13}{2}\right)^{2}}=\sqrt{\frac{81}{4}}$$

Qisqartirish.

$$x+\frac{13}{2}=\frac{9}{2} x+\frac{13}{2}=-\frac{9}{2}$$

Tenglamaning ikkala tarafidan \frac{13}{2} ni ayirish.

$$x=-2 x=-11$$