-793x+9left(x-15right)+4left(x-4right)x/x=0 eching

$$-793x+9 \left( x-15 \right) +4 \left( x-4 \right) \frac{ x }{ x } =0$$

x uchun yechish

$$x=-\frac{151}{780}\approx -0,193589744$$

Faktorlash qadamlari

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

$$-793xx+9\left(x-15\right)x+4\left(x-4\right)x=0$$

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$-793x^{2}+9\left(x-15\right)x+4\left(x-4\right)x=0$$

9 ga x-15 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-793x^{2}+\left(9x-135\right)x+4\left(x-4\right)x=0$$

9x-135 ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-793x^{2}+9x^{2}-135x+4\left(x-4\right)x=0$$

-784x^{2} ni olish uchun -793x^{2} va 9x^{2} ni birlashtirish.

$$-784x^{2}-135x+4\left(x-4\right)x=0$$

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

$$-784x^{2}-135x+\left(4x-16\right)x=0$$

4x-16 ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-784x^{2}-135x+4x^{2}-16x=0$$

-780x^{2} ni olish uchun -784x^{2} va 4x^{2} ni birlashtirish.

$$-780x^{2}-135x-16x=0$$

-151x ni olish uchun -135x va -16x ni birlashtirish.

$$-780x^{2}-151x=0$$

x omili.

$$x\left(-780x-151\right)=0$$

Tenglamani yechish uchun x=0 va -780x-151=0 ni yeching.

$$x=0 x=-\frac{151}{780}$$

x qiymati 0 teng bo‘lmaydi.

$$x=-\frac{151}{780}$$

Kvadrat tenglamalaridan foydalanish qoidalari

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

$$-793xx+9\left(x-15\right)x+4\left(x-4\right)x=0$$

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$-793x^{2}+9\left(x-15\right)x+4\left(x-4\right)x=0$$

9 ga x-15 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-793x^{2}+\left(9x-135\right)x+4\left(x-4\right)x=0$$

9x-135 ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-793x^{2}+9x^{2}-135x+4\left(x-4\right)x=0$$

-784x^{2} ni olish uchun -793x^{2} va 9x^{2} ni birlashtirish.

$$-784x^{2}-135x+4\left(x-4\right)x=0$$

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

$$-784x^{2}-135x+\left(4x-16\right)x=0$$

4x-16 ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-784x^{2}-135x+4x^{2}-16x=0$$

-780x^{2} ni olish uchun -784x^{2} va 4x^{2} ni birlashtirish.

$$-780x^{2}-135x-16x=0$$

-151x ni olish uchun -135x va -16x ni birlashtirish.

$$-780x^{2}-151x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -780 ni a, -151 ni b va 0 ni c bilan almashtiring.

$$x=\frac{-\left(-151\right)±\sqrt{\left(-151\right)^{2}}}{2\left(-780\right)}$$

\left(-151\right)^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-151\right)±151}{2\left(-780\right)}$$

-151 ning teskarisi 151 ga teng.

$$x=\frac{151±151}{2\left(-780\right)}$$

2 ni -780 marotabaga ko'paytirish.

$$x=\frac{151±151}{-1560}$$

x=\frac{151±151}{-1560} tenglamasini yeching, bunda ± musbat. 151 ni 151 ga qo'shish.

$$x=\frac{302}{-1560}$$

\frac{302}{-1560} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=-\frac{151}{780}$$

x=\frac{151±151}{-1560} tenglamasini yeching, bunda ± manfiy. 151 dan 151 ni ayirish.

$$x=\frac{0}{-1560}$$

0 ni -1560 ga bo'lish.

$$x=0$$

Tenglama yechildi.

$$x=-\frac{151}{780} x=0$$

x qiymati 0 teng bo‘lmaydi.

$$x=-\frac{151}{780}$$

Kvadratni yakunlash bo'yicha qadamlar

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

$$-793xx+9\left(x-15\right)x+4\left(x-4\right)x=0$$

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$-793x^{2}+9\left(x-15\right)x+4\left(x-4\right)x=0$$

9 ga x-15 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-793x^{2}+\left(9x-135\right)x+4\left(x-4\right)x=0$$

9x-135 ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-793x^{2}+9x^{2}-135x+4\left(x-4\right)x=0$$

-784x^{2} ni olish uchun -793x^{2} va 9x^{2} ni birlashtirish.

$$-784x^{2}-135x+4\left(x-4\right)x=0$$

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

$$-784x^{2}-135x+\left(4x-16\right)x=0$$

4x-16 ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-784x^{2}-135x+4x^{2}-16x=0$$

-780x^{2} ni olish uchun -784x^{2} va 4x^{2} ni birlashtirish.

$$-780x^{2}-135x-16x=0$$

-151x ni olish uchun -135x va -16x ni birlashtirish.

$$-780x^{2}-151x=0$$

Ikki tarafini -780 ga bo‘ling.

$$\frac{-780x^{2}-151x}{-780}=\frac{0}{-780}$$

-780 ga bo'lish -780 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{151}{-780}\right)x=\frac{0}{-780}$$

-151 ni -780 ga bo'lish.

$$x^{2}+\frac{151}{780}x=\frac{0}{-780}$$

0 ni -780 ga bo'lish.

$$x^{2}+\frac{151}{780}x=0$$

\frac{151}{780} ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{151}{1560} olish uchun. Keyin, \frac{151}{1560} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+\frac{151}{780}x+\left(\frac{151}{1560}\right)^{2}=\left(\frac{151}{1560}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{151}{1560} kvadratini chiqarish.

$$x^{2}+\frac{151}{780}x+\frac{22801}{2433600}=\frac{22801}{2433600}$$

x^{2}+\frac{151}{780}x+\frac{22801}{2433600} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+\frac{151}{1560}\right)^{2}=\frac{22801}{2433600}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{151}{1560}\right)^{2}}=\sqrt{\frac{22801}{2433600}}$$

Qisqartirish.

$$x+\frac{151}{1560}=\frac{151}{1560} x+\frac{151}{1560}=-\frac{151}{1560}$$

Tenglamaning ikkala tarafidan \frac{151}{1560} ni ayirish.

$$x=0 x=-\frac{151}{780}$$

x qiymati 0 teng bo‘lmaydi.

$$x=-\frac{151}{780}$$