-8w^2+2w=0 eching

$$- 8 w ^ { 2 } + 2 w = 0$$

w uchun yechish

$$w=\frac{1}{4}=0,25$$

$$w=0$$

Faktorlash qadamlari

w omili.

$$w\left(-8w+2\right)=0$$

Tenglamani yechish uchun w=0 va -8w+2=0 ni yeching.

$$w=0 w=\frac{1}{4}$$

Kvadrat tenglamalaridan foydalanish qoidalari

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.

$$-8w^{2}+2w=0$$

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

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

2^{2} ning kvadrat ildizini chiqarish.

$$w=\frac{-2±2}{2\left(-8\right)}$$

2 ni -8 marotabaga ko'paytirish.

$$w=\frac{-2±2}{-16}$$

w=\frac{-2±2}{-16} tenglamasini yeching, bunda ± musbat. -2 ni 2 ga qo'shish.

$$w=\frac{0}{-16}$$

0 ni -16 ga bo'lish.

$$w=0$$

w=\frac{-2±2}{-16} tenglamasini yeching, bunda ± manfiy. -2 dan 2 ni ayirish.

$$w=-\frac{4}{-16}$$

\frac{-4}{-16} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$w=\frac{1}{4}$$

Tenglama yechildi.

$$w=0 w=\frac{1}{4}$$

Kvadratni yakunlash bo'yicha qadamlar

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

$$-8w^{2}+2w=0$$

Ikki tarafini -8 ga bo‘ling.

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

-8 ga bo'lish -8 ga ko'paytirishni bekor qiladi.

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

\frac{2}{-8} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$w^{2}-\frac{1}{4}w=\frac{0}{-8}$$

0 ni -8 ga bo'lish.

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

-\frac{1}{4} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{1}{8} olish uchun. Keyin, -\frac{1}{8} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$w^{2}-\frac{1}{4}w+\left(-\frac{1}{8}\right)^{2}=\left(-\frac{1}{8}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{1}{8} kvadratini chiqarish.

$$w^{2}-\frac{1}{4}w+\frac{1}{64}=\frac{1}{64}$$

w^{2}-\frac{1}{4}w+\frac{1}{64} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(w-\frac{1}{8}\right)^{2}=\frac{1}{64}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(w-\frac{1}{8}\right)^{2}}=\sqrt{\frac{1}{64}}$$

Qisqartirish.

$$w-\frac{1}{8}=\frac{1}{8} w-\frac{1}{8}=-\frac{1}{8}$$

\frac{1}{8} ni tenglamaning ikkala tarafiga qo'shish.

$$w=\frac{1}{4} w=0$$