x=2x(x-1) eching

$$x=2x(x-1)$$

x uchun yechish

$$x = \frac{3}{2} = 1\frac{1}{2} = 1,5$$

$$x=0$$

Faktorlash qadamlari

2x ga x-1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

Ikkala tarafdan 2x^{2} ni ayirish.

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

2x ni ikki tarafga qo’shing.

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

3x ni olish uchun x va 2x ni birlashtirish.

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

x omili.

$$x\left(3-2x\right)=0$$

Tenglamani yechish uchun x=0 va 3-2x=0 ni yeching.

$$x=0 x=\frac{3}{2}$$

Kvadrat tenglamalaridan foydalanish qoidalari

2x ga x-1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

Ikkala tarafdan 2x^{2} ni ayirish.

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

2x ni ikki tarafga qo’shing.

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

3x ni olish uchun x va 2x ni birlashtirish.

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

ax^{2}+bx+c=0 shaklidagi barcha tenglamalarni kvadrat formulasi bilan yechish mumkin: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadrat formula ikki yechmni taqdim qiladi, biri ± qo'shish bo'lganda, va ikkinchisi ayiruv bo'lganda.

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

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

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

3^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-3±3}{2\left(-2\right)}$$

2 ni -2 marotabaga ko'paytirish.

$$x=\frac{-3±3}{-4}$$

x=\frac{-3±3}{-4} tenglamasini yeching, bunda ± musbat. -3 ni 3 ga qo'shish.

$$x=\frac{0}{-4}$$

0 ni -4 ga bo'lish.

$$x=0$$

x=\frac{-3±3}{-4} tenglamasini yeching, bunda ± manfiy. -3 dan 3 ni ayirish.

$$x=-\frac{6}{-4}$$

\frac{-6}{-4} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{3}{2}$$

Tenglama yechildi.

$$x=0 x=\frac{3}{2}$$

Kvadratni yakunlash bo'yicha qadamlar

2x ga x-1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

Ikkala tarafdan 2x^{2} ni ayirish.

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

2x ni ikki tarafga qo’shing.

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

3x ni olish uchun x va 2x ni birlashtirish.

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

Bu kabi kvadrat tenglamalarni kvadratni yakunlab yechish mumkin. Kvadratni yechish uchun tenglama avval ushbu shaklda bo'lishi shart: x^{2}+bx=c.

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

Ikki tarafini -2 ga bo‘ling.

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

-2 ga bo'lish -2 ga ko'paytirishni bekor qiladi.

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

3 ni -2 ga bo'lish.

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

0 ni -2 ga bo'lish.

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

-\frac{3}{2} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{3}{4} olish uchun. Keyin, -\frac{3}{4} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

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

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{3}{4} kvadratini chiqarish.

$$x^{2}-\frac{3}{2}x+\frac{9}{16}=\frac{9}{16}$$

x^{2}-\frac{3}{2}x+\frac{9}{16} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{3}{4}\right)^{2}=\frac{9}{16}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{3}{4}\right)^{2}}=\sqrt{\frac{9}{16}}$$

Qisqartirish.

$$x-\frac{3}{4}=\frac{3}{4} x-\frac{3}{4}=-\frac{3}{4}$$

\frac{3}{4} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{3}{2} x=0$$