360/x+156=(x-2)*180 eching

$$\frac{ 360 }{ x } +156=(x-2) \times 180$$

x uchun yechish

$$x = \frac{\sqrt{3649} + 43}{30} \approx 3,446898441$$

$$x=\frac{43-\sqrt{3649}}{30}\approx -0,580231775$$

Kvadrat tenglamalaridan foydalanish qoidalari

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

$$360+x\times 156=\left(x-2\right)\times 180x$$

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

$$360+x\times 156=\left(180x-360\right)x$$

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

$$360+x\times 156=180x^{2}-360x$$

Ikkala tarafdan 180x^{2} ni ayirish.

$$360+x\times 156-180x^{2}=-360x$$

360x ni ikki tarafga qo’shing.

$$360+x\times 156-180x^{2}+360x=0$$

516x ni olish uchun x\times 156 va 360x ni birlashtirish.

$$360+516x-180x^{2}=0$$

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.

$$-180x^{2}+516x+360=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -180 ni a, 516 ni b va 360 ni c bilan almashtiring.

$$x=\frac{-516±\sqrt{516^{2}-4\left(-180\right)\times 360}}{2\left(-180\right)}$$

516 kvadratini chiqarish.

$$x=\frac{-516±\sqrt{266256-4\left(-180\right)\times 360}}{2\left(-180\right)}$$

-4 ni -180 marotabaga ko'paytirish.

$$x=\frac{-516±\sqrt{266256+720\times 360}}{2\left(-180\right)}$$

720 ni 360 marotabaga ko'paytirish.

$$x=\frac{-516±\sqrt{266256+259200}}{2\left(-180\right)}$$

266256 ni 259200 ga qo'shish.

$$x=\frac{-516±\sqrt{525456}}{2\left(-180\right)}$$

525456 ning kvadrat ildizini chiqarish.

$$x=\frac{-516±12\sqrt{3649}}{2\left(-180\right)}$$

2 ni -180 marotabaga ko'paytirish.

$$x=\frac{-516±12\sqrt{3649}}{-360}$$

x=\frac{-516±12\sqrt{3649}}{-360} tenglamasini yeching, bunda ± musbat. -516 ni 12\sqrt{3649} ga qo'shish.

$$x=\frac{12\sqrt{3649}-516}{-360}$$

-516+12\sqrt{3649} ni -360 ga bo'lish.

$$x=\frac{43-\sqrt{3649}}{30}$$

x=\frac{-516±12\sqrt{3649}}{-360} tenglamasini yeching, bunda ± manfiy. -516 dan 12\sqrt{3649} ni ayirish.

$$x=\frac{-12\sqrt{3649}-516}{-360}$$

-516-12\sqrt{3649} ni -360 ga bo'lish.

$$x=\frac{\sqrt{3649}+43}{30}$$

Tenglama yechildi.

$$x=\frac{43-\sqrt{3649}}{30} x=\frac{\sqrt{3649}+43}{30}$$

Kvadratni yakunlash bo'yicha qadamlar

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

$$360+x\times 156=\left(x-2\right)\times 180x$$

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

$$360+x\times 156=\left(180x-360\right)x$$

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

$$360+x\times 156=180x^{2}-360x$$

Ikkala tarafdan 180x^{2} ni ayirish.

$$360+x\times 156-180x^{2}=-360x$$

360x ni ikki tarafga qo’shing.

$$360+x\times 156-180x^{2}+360x=0$$

516x ni olish uchun x\times 156 va 360x ni birlashtirish.

$$360+516x-180x^{2}=0$$

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

$$516x-180x^{2}=-360$$

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

$$-180x^{2}+516x=-360$$

Ikki tarafini -180 ga bo‘ling.

$$\frac{-180x^{2}+516x}{-180}=-\frac{360}{-180}$$

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

$$x^{2}+\frac{516}{-180}x=-\frac{360}{-180}$$

\frac{516}{-180} ulushini 12 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}-\frac{43}{15}x=-\frac{360}{-180}$$

-360 ni -180 ga bo'lish.

$$x^{2}-\frac{43}{15}x=2$$

-\frac{43}{15} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{43}{30} olish uchun. Keyin, -\frac{43}{30} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{43}{15}x+\left(-\frac{43}{30}\right)^{2}=2+\left(-\frac{43}{30}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{43}{30} kvadratini chiqarish.

$$x^{2}-\frac{43}{15}x+\frac{1849}{900}=2+\frac{1849}{900}$$

2 ni \frac{1849}{900} ga qo'shish.

$$x^{2}-\frac{43}{15}x+\frac{1849}{900}=\frac{3649}{900}$$

x^{2}-\frac{43}{15}x+\frac{1849}{900} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{43}{30}\right)^{2}=\frac{3649}{900}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{43}{30}\right)^{2}}=\sqrt{\frac{3649}{900}}$$

Qisqartirish.

$$x-\frac{43}{30}=\frac{\sqrt{3649}}{30} x-\frac{43}{30}=-\frac{\sqrt{3649}}{30}$$

\frac{43}{30} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{\sqrt{3649}+43}{30} x=\frac{43-\sqrt{3649}}{30}$$