left(3x-4right)^2-3x^2=2left(8+13xright) eching

$${ \left(3x-4 \right) }^{ 2 } -3 { x }^{ 2 } = 2 \left( 8+13x \right)$$

x uchun yechish

$$x = \frac{25}{3} = 8\frac{1}{3} \approx 8,333333333$$

$$x=0$$

Faktorlash qadamlari

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(3x-4\right)^{2} kengaytirilishi uchun ishlating.

$$9x^{2}-24x+16-3x^{2}=2\left(8+13x\right)$$

6x^{2} ni olish uchun 9x^{2} va -3x^{2} ni birlashtirish.

$$6x^{2}-24x+16=2\left(8+13x\right)$$

2 ga 8+13x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$6x^{2}-24x+16=16+26x$$

Ikkala tarafdan 16 ni ayirish.

$$6x^{2}-24x+16-16=26x$$

0 olish uchun 16 dan 16 ni ayirish.

$$6x^{2}-24x=26x$$

Ikkala tarafdan 26x ni ayirish.

$$6x^{2}-24x-26x=0$$

-50x ni olish uchun -24x va -26x ni birlashtirish.

$$6x^{2}-50x=0$$

x omili.

$$x\left(6x-50\right)=0$$

Tenglamani yechish uchun x=0 va 6x-50=0 ni yeching.

$$x=0 x=\frac{25}{3}$$

Kvadrat tenglamalaridan foydalanish qoidalari

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(3x-4\right)^{2} kengaytirilishi uchun ishlating.

$$9x^{2}-24x+16-3x^{2}=2\left(8+13x\right)$$

6x^{2} ni olish uchun 9x^{2} va -3x^{2} ni birlashtirish.

$$6x^{2}-24x+16=2\left(8+13x\right)$$

2 ga 8+13x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$6x^{2}-24x+16=16+26x$$

Ikkala tarafdan 16 ni ayirish.

$$6x^{2}-24x+16-16=26x$$

0 olish uchun 16 dan 16 ni ayirish.

$$6x^{2}-24x=26x$$

Ikkala tarafdan 26x ni ayirish.

$$6x^{2}-24x-26x=0$$

-50x ni olish uchun -24x va -26x ni birlashtirish.

$$6x^{2}-50x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 6 ni a, -50 ni b va 0 ni c bilan almashtiring.

$$x=\frac{-\left(-50\right)±\sqrt{\left(-50\right)^{2}}}{2\times 6}$$

\left(-50\right)^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-50\right)±50}{2\times 6}$$

-50 ning teskarisi 50 ga teng.

$$x=\frac{50±50}{2\times 6}$$

2 ni 6 marotabaga ko'paytirish.

$$x=\frac{50±50}{12}$$

x=\frac{50±50}{12} tenglamasini yeching, bunda ± musbat. 50 ni 50 ga qo'shish.

$$x=\frac{100}{12}$$

\frac{100}{12} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{25}{3}$$

x=\frac{50±50}{12} tenglamasini yeching, bunda ± manfiy. 50 dan 50 ni ayirish.

$$x=\frac{0}{12}$$

0 ni 12 ga bo'lish.

$$x=0$$

Tenglama yechildi.

$$x=\frac{25}{3} x=0$$

Kvadratni yakunlash bo'yicha qadamlar

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(3x-4\right)^{2} kengaytirilishi uchun ishlating.

$$9x^{2}-24x+16-3x^{2}=2\left(8+13x\right)$$

6x^{2} ni olish uchun 9x^{2} va -3x^{2} ni birlashtirish.

$$6x^{2}-24x+16=2\left(8+13x\right)$$

2 ga 8+13x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$6x^{2}-24x+16=16+26x$$

Ikkala tarafdan 26x ni ayirish.

$$6x^{2}-24x+16-26x=16$$

-50x ni olish uchun -24x va -26x ni birlashtirish.

$$6x^{2}-50x+16=16$$

Ikkala tarafdan 16 ni ayirish.

$$6x^{2}-50x=16-16$$

0 olish uchun 16 dan 16 ni ayirish.

$$6x^{2}-50x=0$$

Ikki tarafini 6 ga bo‘ling.

$$\frac{6x^{2}-50x}{6}=\frac{0}{6}$$

6 ga bo'lish 6 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{50}{6}\right)x=\frac{0}{6}$$

\frac{-50}{6} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}-\frac{25}{3}x=\frac{0}{6}$$

0 ni 6 ga bo'lish.

$$x^{2}-\frac{25}{3}x=0$$

-\frac{25}{3} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{25}{6} olish uchun. Keyin, -\frac{25}{6} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{25}{3}x+\left(-\frac{25}{6}\right)^{2}=\left(-\frac{25}{6}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{25}{6} kvadratini chiqarish.

$$x^{2}-\frac{25}{3}x+\frac{625}{36}=\frac{625}{36}$$

x^{2}-\frac{25}{3}x+\frac{625}{36} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{25}{6}\right)^{2}=\frac{625}{36}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{25}{6}\right)^{2}}=\sqrt{\frac{625}{36}}$$

Qisqartirish.

$$x-\frac{25}{6}=\frac{25}{6} x-\frac{25}{6}=-\frac{25}{6}$$

\frac{25}{6} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{25}{3} x=0$$