x^2=3x*7(14x+32)*954 eching

$${ x }^{ 2 } =3x \times 7(14x+32) \times 954$$

x uchun yechish

$$x = -\frac{641088}{280475} = -2\frac{80138}{280475} \approx -2,285722435$$

$$x=0$$

Faktorlash qadamlari

21 hosil qilish uchun 3 va 7 ni ko'paytirish.

$$x^{2}=21x\left(14x+32\right)\times 954$$

20034 hosil qilish uchun 21 va 954 ni ko'paytirish.

$$x^{2}=20034x\left(14x+32\right)$$

20034x ga 14x+32 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x^{2}=280476x^{2}+641088x$$

Ikkala tarafdan 280476x^{2} ni ayirish.

$$x^{2}-280476x^{2}=641088x$$

-280475x^{2} ni olish uchun x^{2} va -280476x^{2} ni birlashtirish.

$$-280475x^{2}=641088x$$

Ikkala tarafdan 641088x ni ayirish.

$$-280475x^{2}-641088x=0$$

x omili.

$$x\left(-280475x-641088\right)=0$$

Tenglamani yechish uchun x=0 va -280475x-641088=0 ni yeching.

$$x=0 x=-\frac{641088}{280475}$$

Kvadrat tenglamalaridan foydalanish qoidalari

21 hosil qilish uchun 3 va 7 ni ko'paytirish.

$$x^{2}=21x\left(14x+32\right)\times 954$$

20034 hosil qilish uchun 21 va 954 ni ko'paytirish.

$$x^{2}=20034x\left(14x+32\right)$$

20034x ga 14x+32 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x^{2}=280476x^{2}+641088x$$

Ikkala tarafdan 280476x^{2} ni ayirish.

$$x^{2}-280476x^{2}=641088x$$

-280475x^{2} ni olish uchun x^{2} va -280476x^{2} ni birlashtirish.

$$-280475x^{2}=641088x$$

Ikkala tarafdan 641088x ni ayirish.

$$-280475x^{2}-641088x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -280475 ni a, -641088 ni b va 0 ni c bilan almashtiring.

$$x=\frac{-\left(-641088\right)±\sqrt{\left(-641088\right)^{2}}}{2\left(-280475\right)}$$

\left(-641088\right)^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-641088\right)±641088}{2\left(-280475\right)}$$

-641088 ning teskarisi 641088 ga teng.

$$x=\frac{641088±641088}{2\left(-280475\right)}$$

2 ni -280475 marotabaga ko'paytirish.

$$x=\frac{641088±641088}{-560950}$$

x=\frac{641088±641088}{-560950} tenglamasini yeching, bunda ± musbat. 641088 ni 641088 ga qo'shish.

$$x=\frac{1282176}{-560950}$$

\frac{1282176}{-560950} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=-\frac{641088}{280475}$$

x=\frac{641088±641088}{-560950} tenglamasini yeching, bunda ± manfiy. 641088 dan 641088 ni ayirish.

$$x=\frac{0}{-560950}$$

0 ni -560950 ga bo'lish.

$$x=0$$

Tenglama yechildi.

$$x=-\frac{641088}{280475} x=0$$

Kvadratni yakunlash bo'yicha qadamlar

21 hosil qilish uchun 3 va 7 ni ko'paytirish.

$$x^{2}=21x\left(14x+32\right)\times 954$$

20034 hosil qilish uchun 21 va 954 ni ko'paytirish.

$$x^{2}=20034x\left(14x+32\right)$$

20034x ga 14x+32 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x^{2}=280476x^{2}+641088x$$

Ikkala tarafdan 280476x^{2} ni ayirish.

$$x^{2}-280476x^{2}=641088x$$

-280475x^{2} ni olish uchun x^{2} va -280476x^{2} ni birlashtirish.

$$-280475x^{2}=641088x$$

Ikkala tarafdan 641088x ni ayirish.

$$-280475x^{2}-641088x=0$$

Ikki tarafini -280475 ga bo‘ling.

$$\frac{-280475x^{2}-641088x}{-280475}=\frac{0}{-280475}$$

-280475 ga bo'lish -280475 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{641088}{-280475}\right)x=\frac{0}{-280475}$$

-641088 ni -280475 ga bo'lish.

$$x^{2}+\frac{641088}{280475}x=\frac{0}{-280475}$$

0 ni -280475 ga bo'lish.

$$x^{2}+\frac{641088}{280475}x=0$$

\frac{641088}{280475} ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{320544}{280475} olish uchun. Keyin, \frac{320544}{280475} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+\frac{641088}{280475}x+\left(\frac{320544}{280475}\right)^{2}=\left(\frac{320544}{280475}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{320544}{280475} kvadratini chiqarish.

$$x^{2}+\frac{641088}{280475}x+\frac{102748455936}{78666225625}=\frac{102748455936}{78666225625}$$

x^{2}+\frac{641088}{280475}x+\frac{102748455936}{78666225625} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+\frac{320544}{280475}\right)^{2}=\frac{102748455936}{78666225625}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{320544}{280475}\right)^{2}}=\sqrt{\frac{102748455936}{78666225625}}$$

Qisqartirish.

$$x+\frac{320544}{280475}=\frac{320544}{280475} x+\frac{320544}{280475}=-\frac{320544}{280475}$$

Tenglamaning ikkala tarafidan \frac{320544}{280475} ni ayirish.

$$x=0 x=-\frac{641088}{280475}$$