94w^2+42w=0 eching

$$94 w ^ { 2 } + 42 w = 0$$

w uchun yechish

$$w=-\frac{21}{47}\approx -0,446808511$$

$$w=0$$

Faktorlash qadamlari

w omili.

$$w\left(94w+42\right)=0$$

Tenglamani yechish uchun w=0 va 94w+42=0 ni yeching.

$$w=0 w=-\frac{21}{47}$$

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.

$$94w^{2}+42w=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 94 ni a, 42 ni b va 0 ni c bilan almashtiring.

$$w=\frac{-42±\sqrt{42^{2}}}{2\times 94}$$

42^{2} ning kvadrat ildizini chiqarish.

$$w=\frac{-42±42}{2\times 94}$$

2 ni 94 marotabaga ko'paytirish.

$$w=\frac{-42±42}{188}$$

w=\frac{-42±42}{188} tenglamasini yeching, bunda ± musbat. -42 ni 42 ga qo'shish.

$$w=\frac{0}{188}$$

0 ni 188 ga bo'lish.

$$w=0$$

w=\frac{-42±42}{188} tenglamasini yeching, bunda ± manfiy. -42 dan 42 ni ayirish.

$$w=-\frac{84}{188}$$

\frac{-84}{188} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$w=-\frac{21}{47}$$

Tenglama yechildi.

$$w=0 w=-\frac{21}{47}$$

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.

$$94w^{2}+42w=0$$

Ikki tarafini 94 ga bo‘ling.

$$\frac{94w^{2}+42w}{94}=\frac{0}{94}$$

94 ga bo'lish 94 ga ko'paytirishni bekor qiladi.

$$w^{2}+\frac{42}{94}w=\frac{0}{94}$$

\frac{42}{94} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$w^{2}+\frac{21}{47}w=\frac{0}{94}$$

0 ni 94 ga bo'lish.

$$w^{2}+\frac{21}{47}w=0$$

\frac{21}{47} ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{21}{94} olish uchun. Keyin, \frac{21}{94} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$w^{2}+\frac{21}{47}w+\left(\frac{21}{94}\right)^{2}=\left(\frac{21}{94}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{21}{94} kvadratini chiqarish.

$$w^{2}+\frac{21}{47}w+\frac{441}{8836}=\frac{441}{8836}$$

w^{2}+\frac{21}{47}w+\frac{441}{8836} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(w+\frac{21}{94}\right)^{2}=\frac{441}{8836}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(w+\frac{21}{94}\right)^{2}}=\sqrt{\frac{441}{8836}}$$

Qisqartirish.

$$w+\frac{21}{94}=\frac{21}{94} w+\frac{21}{94}=-\frac{21}{94}$$

Tenglamaning ikkala tarafidan \frac{21}{94} ni ayirish.

$$w=0 w=-\frac{21}{47}$$