x=4x^2-x eching

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

x uchun yechish

$$x=\frac{1}{2}=0,5$$

$$x=0$$

Faktorlash qadamlari

Ikkala tarafdan 4x^{2} ni ayirish.

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

x ni ikki tarafga qo’shing.

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

2x ni olish uchun x va x ni birlashtirish.

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

x omili.

$$x\left(2-4x\right)=0$$

Tenglamani yechish uchun x=0 va 2-4x=0 ni yeching.

$$x=0 x=\frac{1}{2}$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 4x^{2} ni ayirish.

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

x ni ikki tarafga qo’shing.

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

2x ni olish uchun x va x ni birlashtirish.

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

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.

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

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

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

2^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-2±2}{2\left(-4\right)}$$

2 ni -4 marotabaga ko'paytirish.

$$x=\frac{-2±2}{-8}$$

x=\frac{-2±2}{-8} tenglamasini yeching, bunda ± musbat. -2 ni 2 ga qo'shish.

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

0 ni -8 ga bo'lish.

$$x=0$$

x=\frac{-2±2}{-8} tenglamasini yeching, bunda ± manfiy. -2 dan 2 ni ayirish.

$$x=-\frac{4}{-8}$$

\frac{-4}{-8} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{1}{2}$$

Tenglama yechildi.

$$x=0 x=\frac{1}{2}$$

Kvadratni yakunlash bo'yicha qadamlar

Ikkala tarafdan 4x^{2} ni ayirish.

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

x ni ikki tarafga qo’shing.

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

2x ni olish uchun x va x ni birlashtirish.

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

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

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

Ikki tarafini -4 ga bo‘ling.

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

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

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

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

$$x^{2}-\frac{1}{2}x=\frac{0}{-4}$$

0 ni -4 ga bo'lish.

$$x^{2}-\frac{1}{2}x=0$$

-\frac{1}{2} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{1}{4} olish uchun. Keyin, -\frac{1}{4} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{1}{2}x+\left(-\frac{1}{4}\right)^{2}=\left(-\frac{1}{4}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{1}{4} kvadratini chiqarish.

$$x^{2}-\frac{1}{2}x+\frac{1}{16}=\frac{1}{16}$$

x^{2}-\frac{1}{2}x+\frac{1}{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.

$$\left(x-\frac{1}{4}\right)^{2}=\frac{1}{16}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{1}{4}\right)^{2}}=\sqrt{\frac{1}{16}}$$

Qisqartirish.

$$x-\frac{1}{4}=\frac{1}{4} x-\frac{1}{4}=-\frac{1}{4}$$

\frac{1}{4} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{1}{2} x=0$$