4=x^2/(109-x)*(083-x) eching

$$4= \frac{ { x }^{ 2 } }{ (109-x) \times (083-x) }$$

x uchun yechish

$$x = \frac{436}{3} = 145\frac{1}{3} \approx 145,333333333$$

Faktorlash qadamlari

x qiymati 0,109 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x\left(x-109\right) ga ko'paytirish.

$$4x\left(x-109\right)=x^{2}$$

4x ga x-109 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$4x^{2}-436x=x^{2}$$

Ikkala tarafdan x^{2} ni ayirish.

$$4x^{2}-436x-x^{2}=0$$

3x^{2} ni olish uchun 4x^{2} va -x^{2} ni birlashtirish.

$$3x^{2}-436x=0$$

x omili.

$$x\left(3x-436\right)=0$$

Tenglamani yechish uchun x=0 va 3x-436=0 ni yeching.

$$x=0 x=\frac{436}{3}$$

x qiymati 0 teng bo‘lmaydi.

$$x=\frac{436}{3}$$

Kvadrat tenglamalaridan foydalanish qoidalari

x qiymati 0,109 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x\left(x-109\right) ga ko'paytirish.

$$4x\left(x-109\right)=x^{2}$$

4x ga x-109 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$4x^{2}-436x=x^{2}$$

Ikkala tarafdan x^{2} ni ayirish.

$$4x^{2}-436x-x^{2}=0$$

3x^{2} ni olish uchun 4x^{2} va -x^{2} ni birlashtirish.

$$3x^{2}-436x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 3 ni a, -436 ni b va 0 ni c bilan almashtiring.

$$x=\frac{-\left(-436\right)±\sqrt{\left(-436\right)^{2}}}{2\times 3}$$

\left(-436\right)^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-436\right)±436}{2\times 3}$$

-436 ning teskarisi 436 ga teng.

$$x=\frac{436±436}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$x=\frac{436±436}{6}$$

x=\frac{436±436}{6} tenglamasini yeching, bunda ± musbat. 436 ni 436 ga qo'shish.

$$x=\frac{872}{6}$$

\frac{872}{6} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{436}{3}$$

x=\frac{436±436}{6} tenglamasini yeching, bunda ± manfiy. 436 dan 436 ni ayirish.

$$x=\frac{0}{6}$$

0 ni 6 ga bo'lish.

$$x=0$$

Tenglama yechildi.

$$x=\frac{436}{3} x=0$$

x qiymati 0 teng bo‘lmaydi.

$$x=\frac{436}{3}$$

Kvadratni yakunlash bo'yicha qadamlar

x qiymati 0,109 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x\left(x-109\right) ga ko'paytirish.

$$4x\left(x-109\right)=x^{2}$$

4x ga x-109 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$4x^{2}-436x=x^{2}$$

Ikkala tarafdan x^{2} ni ayirish.

$$4x^{2}-436x-x^{2}=0$$

3x^{2} ni olish uchun 4x^{2} va -x^{2} ni birlashtirish.

$$3x^{2}-436x=0$$

Ikki tarafini 3 ga bo‘ling.

$$\frac{3x^{2}-436x}{3}=\frac{0}{3}$$

3 ga bo'lish 3 ga ko'paytirishni bekor qiladi.

$$x^{2}-\frac{436}{3}x=\frac{0}{3}$$

0 ni 3 ga bo'lish.

$$x^{2}-\frac{436}{3}x=0$$

-\frac{436}{3} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{218}{3} olish uchun. Keyin, -\frac{218}{3} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{436}{3}x+\left(-\frac{218}{3}\right)^{2}=\left(-\frac{218}{3}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{218}{3} kvadratini chiqarish.

$$x^{2}-\frac{436}{3}x+\frac{47524}{9}=\frac{47524}{9}$$

x^{2}-\frac{436}{3}x+\frac{47524}{9} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{218}{3}\right)^{2}=\frac{47524}{9}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{218}{3}\right)^{2}}=\sqrt{\frac{47524}{9}}$$

Qisqartirish.

$$x-\frac{218}{3}=\frac{218}{3} x-\frac{218}{3}=-\frac{218}{3}$$

\frac{218}{3} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{436}{3} x=0$$

x qiymati 0 teng bo‘lmaydi.

$$x=\frac{436}{3}$$