180*(x-2)-180(x-2)/x=180 eching

$$180 \times (x-2)- \frac{ 180(x-2) }{ x } =180$$

x uchun yechish

$$x=\sqrt{2}+2\approx 3,414213562$$

$$x=2-\sqrt{2}\approx 0,585786438$$

Kvadrat tenglamalaridan foydalanish qoidalari

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

$$180\left(x-2\right)x-180\left(x-2\right)=180x$$

180 ga x-2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(180x-360\right)x-180\left(x-2\right)=180x$$

180x-360 ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$180x^{2}-360x-180\left(x-2\right)=180x$$

-180 ga x-2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$180x^{2}-360x-180x+360=180x$$

-540x ni olish uchun -360x va -180x ni birlashtirish.

$$180x^{2}-540x+360=180x$$

Ikkala tarafdan 180x ni ayirish.

$$180x^{2}-540x+360-180x=0$$

-720x ni olish uchun -540x va -180x ni birlashtirish.

$$180x^{2}-720x+360=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 180 ni a, -720 ni b va 360 ni c bilan almashtiring.

$$x=\frac{-\left(-720\right)±\sqrt{\left(-720\right)^{2}-4\times 180\times 360}}{2\times 180}$$

-720 kvadratini chiqarish.

$$x=\frac{-\left(-720\right)±\sqrt{518400-4\times 180\times 360}}{2\times 180}$$

-4 ni 180 marotabaga ko'paytirish.

$$x=\frac{-\left(-720\right)±\sqrt{518400-720\times 360}}{2\times 180}$$

-720 ni 360 marotabaga ko'paytirish.

$$x=\frac{-\left(-720\right)±\sqrt{518400-259200}}{2\times 180}$$

518400 ni -259200 ga qo'shish.

$$x=\frac{-\left(-720\right)±\sqrt{259200}}{2\times 180}$$

259200 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-720\right)±360\sqrt{2}}{2\times 180}$$

-720 ning teskarisi 720 ga teng.

$$x=\frac{720±360\sqrt{2}}{2\times 180}$$

2 ni 180 marotabaga ko'paytirish.

$$x=\frac{720±360\sqrt{2}}{360}$$

x=\frac{720±360\sqrt{2}}{360} tenglamasini yeching, bunda ± musbat. 720 ni 360\sqrt{2} ga qo'shish.

$$x=\frac{360\sqrt{2}+720}{360}$$

720+360\sqrt{2} ni 360 ga bo'lish.

$$x=\sqrt{2}+2$$

x=\frac{720±360\sqrt{2}}{360} tenglamasini yeching, bunda ± manfiy. 720 dan 360\sqrt{2} ni ayirish.

$$x=\frac{720-360\sqrt{2}}{360}$$

720-360\sqrt{2} ni 360 ga bo'lish.

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

Tenglama yechildi.

$$x=\sqrt{2}+2 x=2-\sqrt{2}$$

Kvadratni yakunlash bo'yicha qadamlar

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

$$180\left(x-2\right)x-180\left(x-2\right)=180x$$

180 ga x-2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(180x-360\right)x-180\left(x-2\right)=180x$$

180x-360 ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$180x^{2}-360x-180\left(x-2\right)=180x$$

-180 ga x-2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$180x^{2}-360x-180x+360=180x$$

-540x ni olish uchun -360x va -180x ni birlashtirish.

$$180x^{2}-540x+360=180x$$

Ikkala tarafdan 180x ni ayirish.

$$180x^{2}-540x+360-180x=0$$

-720x ni olish uchun -540x va -180x ni birlashtirish.

$$180x^{2}-720x+360=0$$

Ikkala tarafdan 360 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$180x^{2}-720x=-360$$

Ikki tarafini 180 ga bo‘ling.

$$\frac{180x^{2}-720x}{180}=-\frac{360}{180}$$

180 ga bo'lish 180 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{720}{180}\right)x=-\frac{360}{180}$$

-720 ni 180 ga bo'lish.

$$x^{2}-4x=-\frac{360}{180}$$

-360 ni 180 ga bo'lish.

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

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

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

-2 kvadratini chiqarish.

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

-2 ni 4 ga qo'shish.

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

x^{2}-4x+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.

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

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

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

Qisqartirish.

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

2 ni tenglamaning ikkala tarafiga qo'shish.

$$x=\sqrt{2}+2 x=2-\sqrt{2}$$