6w^2-18w=0 eching

$$6 w ^ { 2 } - 18 w = 0$$

w uchun yechish

$$w=3$$

$$w=0$$

Faktorlash qadamlari

w omili.

$$w\left(6w-18\right)=0$$

Tenglamani yechish uchun w=0 va 6w-18=0 ni yeching.

$$w=0 w=3$$

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.

$$6w^{2}-18w=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 6 ni a, -18 ni b va 0 ni c bilan almashtiring.

$$w=\frac{-\left(-18\right)±\sqrt{\left(-18\right)^{2}}}{2\times 6}$$

\left(-18\right)^{2} ning kvadrat ildizini chiqarish.

$$w=\frac{-\left(-18\right)±18}{2\times 6}$$

-18 ning teskarisi 18 ga teng.

$$w=\frac{18±18}{2\times 6}$$

2 ni 6 marotabaga ko'paytirish.

$$w=\frac{18±18}{12}$$

w=\frac{18±18}{12} tenglamasini yeching, bunda ± musbat. 18 ni 18 ga qo'shish.

$$w=\frac{36}{12}$$

36 ni 12 ga bo'lish.

$$w=3$$

w=\frac{18±18}{12} tenglamasini yeching, bunda ± manfiy. 18 dan 18 ni ayirish.

$$w=\frac{0}{12}$$

0 ni 12 ga bo'lish.

$$w=0$$

Tenglama yechildi.

$$w=3 w=0$$

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.

$$6w^{2}-18w=0$$

Ikki tarafini 6 ga bo‘ling.

$$\frac{6w^{2}-18w}{6}=\frac{0}{6}$$

6 ga bo'lish 6 ga ko'paytirishni bekor qiladi.

$$w^{2}+\left(-\frac{18}{6}\right)w=\frac{0}{6}$$

-18 ni 6 ga bo'lish.

$$w^{2}-3w=\frac{0}{6}$$

0 ni 6 ga bo'lish.

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

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

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

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{3}{2} kvadratini chiqarish.

$$w^{2}-3w+\frac{9}{4}=\frac{9}{4}$$

w^{2}-3w+\frac{9}{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.

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

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

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

Qisqartirish.

$$w-\frac{3}{2}=\frac{3}{2} w-\frac{3}{2}=-\frac{3}{2}$$

\frac{3}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$w=3 w=0$$