2x-7/x+3=7 eching

$$2 x - \frac { 7 } { x + 3 } = 7$$

x uchun yechish

$$x = -\frac{7}{2} = -3\frac{1}{2} = -3,5$$

$$x=4$$

Kvadrat tenglamalaridan foydalanish qoidalari

x qiymati -3 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x+3 ga ko'paytirish.

$$2x\left(x+3\right)-7=7\left(x+3\right)$$

2x ga x+3 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$2x^{2}+6x-7=7\left(x+3\right)$$

7 ga x+3 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$2x^{2}+6x-7=7x+21$$

Ikkala tarafdan 7x ni ayirish.

$$2x^{2}+6x-7-7x=21$$

-x ni olish uchun 6x va -7x ni birlashtirish.

$$2x^{2}-x-7=21$$

Ikkala tarafdan 21 ni ayirish.

$$2x^{2}-x-7-21=0$$

-28 olish uchun -7 dan 21 ni ayirish.

$$2x^{2}-x-28=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 2 ni a, -1 ni b va -28 ni c bilan almashtiring.

$$x=\frac{-\left(-1\right)±\sqrt{1-4\times 2\left(-28\right)}}{2\times 2}$$

-4 ni 2 marotabaga ko'paytirish.

$$x=\frac{-\left(-1\right)±\sqrt{1-8\left(-28\right)}}{2\times 2}$$

-8 ni -28 marotabaga ko'paytirish.

$$x=\frac{-\left(-1\right)±\sqrt{1+224}}{2\times 2}$$

1 ni 224 ga qo'shish.

$$x=\frac{-\left(-1\right)±\sqrt{225}}{2\times 2}$$

225 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-1\right)±15}{2\times 2}$$

-1 ning teskarisi 1 ga teng.

$$x=\frac{1±15}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$x=\frac{1±15}{4}$$

x=\frac{1±15}{4} tenglamasini yeching, bunda ± musbat. 1 ni 15 ga qo'shish.

$$x=\frac{16}{4}$$

16 ni 4 ga bo'lish.

$$x=4$$

x=\frac{1±15}{4} tenglamasini yeching, bunda ± manfiy. 1 dan 15 ni ayirish.

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

\frac{-14}{4} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

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

Tenglama yechildi.

$$x=4 x=-\frac{7}{2}$$

Kvadratni yakunlash bo'yicha qadamlar

x qiymati -3 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x+3 ga ko'paytirish.

$$2x\left(x+3\right)-7=7\left(x+3\right)$$

2x ga x+3 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$2x^{2}+6x-7=7\left(x+3\right)$$

7 ga x+3 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$2x^{2}+6x-7=7x+21$$

Ikkala tarafdan 7x ni ayirish.

$$2x^{2}+6x-7-7x=21$$

-x ni olish uchun 6x va -7x ni birlashtirish.

$$2x^{2}-x-7=21$$

7 ni ikki tarafga qo’shing.

$$2x^{2}-x=21+7$$

28 olish uchun 21 va 7'ni qo'shing.

$$2x^{2}-x=28$$

Ikki tarafini 2 ga bo‘ling.

$$\frac{2x^{2}-x}{2}=\frac{28}{2}$$

2 ga bo'lish 2 ga ko'paytirishni bekor qiladi.

$$x^{2}-\frac{1}{2}x=\frac{28}{2}$$

28 ni 2 ga bo'lish.

$$x^{2}-\frac{1}{2}x=14$$

-\frac{1}{2} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{1}{4} olish uchun. Keyin, -\frac{1}{4} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{1}{2}x+\left(-\frac{1}{4}\right)^{2}=14+\left(-\frac{1}{4}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{1}{4} kvadratini chiqarish.

$$x^{2}-\frac{1}{2}x+\frac{1}{16}=14+\frac{1}{16}$$

14 ni \frac{1}{16} ga qo'shish.

$$x^{2}-\frac{1}{2}x+\frac{1}{16}=\frac{225}{16}$$

x^{2}-\frac{1}{2}x+\frac{1}{16} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{1}{4}\right)^{2}=\frac{225}{16}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{1}{4}\right)^{2}}=\sqrt{\frac{225}{16}}$$

Qisqartirish.

$$x-\frac{1}{4}=\frac{15}{4} x-\frac{1}{4}=-\frac{15}{4}$$

\frac{1}{4} ni tenglamaning ikkala tarafiga qo'shish.

$$x=4 x=-\frac{7}{2}$$