8x=4x^2 eching

$$8 x = 4 x ^ { 2 }$$

x uchun yechish

$$x=2$$

$$x=0$$

Faktorlash qadamlari

Ikkala tarafdan 4x^{2} ni ayirish.

$$8x-4x^{2}=0$$

x omili.

$$x\left(8-4x\right)=0$$

Tenglamani yechish uchun x=0 va 8-4x=0 ni yeching.

$$x=0 x=2$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 4x^{2} ni ayirish.

$$8x-4x^{2}=0$$

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.

$$-4x^{2}+8x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -4 ni a, 8 ni b va 0 ni c bilan almashtiring.

$$x=\frac{-8±\sqrt{8^{2}}}{2\left(-4\right)}$$

8^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-8±8}{2\left(-4\right)}$$

2 ni -4 marotabaga ko'paytirish.

$$x=\frac{-8±8}{-8}$$

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

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

0 ni -8 ga bo'lish.

$$x=0$$

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

$$x=-\frac{16}{-8}$$

-16 ni -8 ga bo'lish.

$$x=2$$

Tenglama yechildi.

$$x=0 x=2$$

Kvadratni yakunlash bo'yicha qadamlar

Ikkala tarafdan 4x^{2} ni ayirish.

$$8x-4x^{2}=0$$

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

$$-4x^{2}+8x=0$$

Ikki tarafini -4 ga bo‘ling.

$$\frac{-4x^{2}+8x}{-4}=\frac{0}{-4}$$

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

$$x^{2}+\frac{8}{-4}x=\frac{0}{-4}$$

8 ni -4 ga bo'lish.

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

0 ni -4 ga bo'lish.

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

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

$$x^{2}-2x+1=1$$

x^{2}-2x+1 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

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

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

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

Qisqartirish.

$$x-1=1 x-1=-1$$

1 ni tenglamaning ikkala tarafiga qo'shish.

$$x=2 x=0$$