4x(x-3)=16x eching

$$4 x ( x - 3 ) = 16 x$$

x uchun yechish

$$x=7$$

$$x=0$$

Faktorlash qadamlari

4x ga x-3 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$4x^{2}-12x=16x$$

Ikkala tarafdan 16x ni ayirish.

$$4x^{2}-12x-16x=0$$

-28x ni olish uchun -12x va -16x ni birlashtirish.

$$4x^{2}-28x=0$$

x omili.

$$x\left(4x-28\right)=0$$

Tenglamani yechish uchun x=0 va 4x-28=0 ni yeching.

$$x=0 x=7$$

Kvadrat tenglamalaridan foydalanish qoidalari

4x ga x-3 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$4x^{2}-12x=16x$$

Ikkala tarafdan 16x ni ayirish.

$$4x^{2}-12x-16x=0$$

-28x ni olish uchun -12x va -16x ni birlashtirish.

$$4x^{2}-28x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 4 ni a, -28 ni b va 0 ni c bilan almashtiring.

$$x=\frac{-\left(-28\right)±\sqrt{\left(-28\right)^{2}}}{2\times 4}$$

\left(-28\right)^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-28\right)±28}{2\times 4}$$

-28 ning teskarisi 28 ga teng.

$$x=\frac{28±28}{2\times 4}$$

2 ni 4 marotabaga ko'paytirish.

$$x=\frac{28±28}{8}$$

x=\frac{28±28}{8} tenglamasini yeching, bunda ± musbat. 28 ni 28 ga qo'shish.

$$x=\frac{56}{8}$$

56 ni 8 ga bo'lish.

$$x=7$$

x=\frac{28±28}{8} tenglamasini yeching, bunda ± manfiy. 28 dan 28 ni ayirish.

$$x=\frac{0}{8}$$

0 ni 8 ga bo'lish.

$$x=0$$

Tenglama yechildi.

$$x=7 x=0$$

Kvadratni yakunlash bo'yicha qadamlar

4x ga x-3 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$4x^{2}-12x=16x$$

Ikkala tarafdan 16x ni ayirish.

$$4x^{2}-12x-16x=0$$

-28x ni olish uchun -12x va -16x ni birlashtirish.

$$4x^{2}-28x=0$$

Ikki tarafini 4 ga bo‘ling.

$$\frac{4x^{2}-28x}{4}=\frac{0}{4}$$

4 ga bo'lish 4 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{28}{4}\right)x=\frac{0}{4}$$

-28 ni 4 ga bo'lish.

$$x^{2}-7x=\frac{0}{4}$$

0 ni 4 ga bo'lish.

$$x^{2}-7x=0$$

-7 ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{7}{2} olish uchun. Keyin, -\frac{7}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-7x+\left(-\frac{7}{2}\right)^{2}=\left(-\frac{7}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{7}{2} kvadratini chiqarish.

$$x^{2}-7x+\frac{49}{4}=\frac{49}{4}$$

x^{2}-7x+\frac{49}{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.

$$\left(x-\frac{7}{2}\right)^{2}=\frac{49}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{7}{2}\right)^{2}}=\sqrt{\frac{49}{4}}$$

Qisqartirish.

$$x-\frac{7}{2}=\frac{7}{2} x-\frac{7}{2}=-\frac{7}{2}$$

\frac{7}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$x=7 x=0$$