(-3x+1)(x-4)=x-4 eching

$$(-3x+1)(x-4)=x-4$$

x uchun yechish

$$x=4$$

$$x=0$$

Kvadrat tenglamalaridan foydalanish qoidalari

-3x+1 ga x-4 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$-3x^{2}+13x-4=x-4$$

Ikkala tarafdan x ni ayirish.

$$-3x^{2}+13x-4-x=-4$$

12x ni olish uchun 13x va -x ni birlashtirish.

$$-3x^{2}+12x-4=-4$$

4 ni ikki tarafga qo’shing.

$$-3x^{2}+12x-4+4=0$$

0 olish uchun -4 va 4'ni qo'shing.

$$-3x^{2}+12x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -3 ni a, 12 ni b va 0 ni c bilan almashtiring.

$$x=\frac{-12±\sqrt{12^{2}}}{2\left(-3\right)}$$

12^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-12±12}{2\left(-3\right)}$$

2 ni -3 marotabaga ko'paytirish.

$$x=\frac{-12±12}{-6}$$

x=\frac{-12±12}{-6} tenglamasini yeching, bunda ± musbat. -12 ni 12 ga qo'shish.

$$x=\frac{0}{-6}$$

0 ni -6 ga bo'lish.

$$x=0$$

x=\frac{-12±12}{-6} tenglamasini yeching, bunda ± manfiy. -12 dan 12 ni ayirish.

$$x=-\frac{24}{-6}$$

-24 ni -6 ga bo'lish.

$$x=4$$

Tenglama yechildi.

$$x=0 x=4$$

Kvadratni yakunlash bo'yicha qadamlar

-3x+1 ga x-4 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$-3x^{2}+13x-4=x-4$$

Ikkala tarafdan x ni ayirish.

$$-3x^{2}+13x-4-x=-4$$

12x ni olish uchun 13x va -x ni birlashtirish.

$$-3x^{2}+12x-4=-4$$

4 ni ikki tarafga qo’shing.

$$-3x^{2}+12x=-4+4$$

0 olish uchun -4 va 4'ni qo'shing.

$$-3x^{2}+12x=0$$

Ikki tarafini -3 ga bo‘ling.

$$\frac{-3x^{2}+12x}{-3}=\frac{0}{-3}$$

-3 ga bo'lish -3 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{12}{-3}x=\frac{0}{-3}$$

12 ni -3 ga bo'lish.

$$x^{2}-4x=\frac{0}{-3}$$

0 ni -3 ga bo'lish.

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

-4 ni bo‘lish, x shartining koeffitsienti, 2 ga -2 olish uchun. Keyin, -2 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

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

-2 kvadratini chiqarish.

$$x^{2}-4x+4=4$$

x^{2}-4x+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.

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

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

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

Qisqartirish.

$$x-2=2 x-2=-2$$

2 ni tenglamaning ikkala tarafiga qo'shish.

$$x=4 x=0$$