35/x-3=x-7/4 eching

$$\frac{ 35 }{ x-3 } = \frac{ x-7 }{ 4 }$$

x uchun yechish

$$x=-7$$

$$x=17$$

Kvadrat tenglamalaridan foydalanish qoidalari

x qiymati 3 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 4\left(x-3\right) ga, x-3,4 ning eng kichik karralisiga ko‘paytiring.

$$4\times 35=\left(x-3\right)\left(x-7\right)$$

140 hosil qilish uchun 4 va 35 ni ko'paytirish.

$$140=\left(x-3\right)\left(x-7\right)$$

x-3 ga x-7 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$140=x^{2}-10x+21$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$x^{2}-10x+21=140$$

Ikkala tarafdan 140 ni ayirish.

$$x^{2}-10x+21-140=0$$

-119 olish uchun 21 dan 140 ni ayirish.

$$x^{2}-10x-119=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -10 ni b va -119 ni c bilan almashtiring.

$$x=\frac{-\left(-10\right)±\sqrt{\left(-10\right)^{2}-4\left(-119\right)}}{2}$$

-10 kvadratini chiqarish.

$$x=\frac{-\left(-10\right)±\sqrt{100-4\left(-119\right)}}{2}$$

-4 ni -119 marotabaga ko'paytirish.

$$x=\frac{-\left(-10\right)±\sqrt{100+476}}{2}$$

100 ni 476 ga qo'shish.

$$x=\frac{-\left(-10\right)±\sqrt{576}}{2}$$

576 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-10\right)±24}{2}$$

-10 ning teskarisi 10 ga teng.

$$x=\frac{10±24}{2}$$

x=\frac{10±24}{2} tenglamasini yeching, bunda ± musbat. 10 ni 24 ga qo'shish.

$$x=\frac{34}{2}$$

34 ni 2 ga bo'lish.

$$x=17$$

x=\frac{10±24}{2} tenglamasini yeching, bunda ± manfiy. 10 dan 24 ni ayirish.

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

-14 ni 2 ga bo'lish.

$$x=-7$$

Tenglama yechildi.

$$x=17 x=-7$$

Kvadratni yakunlash bo'yicha qadamlar

x qiymati 3 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 4\left(x-3\right) ga, x-3,4 ning eng kichik karralisiga ko‘paytiring.

$$4\times 35=\left(x-3\right)\left(x-7\right)$$

140 hosil qilish uchun 4 va 35 ni ko'paytirish.

$$140=\left(x-3\right)\left(x-7\right)$$

x-3 ga x-7 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$140=x^{2}-10x+21$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$x^{2}-10x+21=140$$

Ikkala tarafdan 21 ni ayirish.

$$x^{2}-10x=140-21$$

119 olish uchun 140 dan 21 ni ayirish.

$$x^{2}-10x=119$$

-10 ni bo‘lish, x shartining koeffitsienti, 2 ga -5 olish uchun. Keyin, -5 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-10x+\left(-5\right)^{2}=119+\left(-5\right)^{2}$$

-5 kvadratini chiqarish.

$$x^{2}-10x+25=119+25$$

119 ni 25 ga qo'shish.

$$x^{2}-10x+25=144$$

x^{2}-10x+25 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-5\right)^{2}=144$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-5\right)^{2}}=\sqrt{144}$$

Qisqartirish.

$$x-5=12 x-5=-12$$

5 ni tenglamaning ikkala tarafiga qo'shish.

$$x=17 x=-7$$