96x^2-x=0 eching

$$96 x ^ { 2 } - x = 0$$

x uchun yechish

$$x=\frac{1}{96}\approx 0,010416667$$

$$x=0$$

Faktorlash qadamlari

x omili.

$$x\left(96x-1\right)=0$$

Tenglamani yechish uchun x=0 va 96x-1=0 ni yeching.

$$x=0 x=\frac{1}{96}$$

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.

$$96x^{2}-x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 96 ni a, -1 ni b va 0 ni c bilan almashtiring.

$$x=\frac{-\left(-1\right)±\sqrt{1}}{2\times 96}$$

1 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-1\right)±1}{2\times 96}$$

-1 ning teskarisi 1 ga teng.

$$x=\frac{1±1}{2\times 96}$$

2 ni 96 marotabaga ko'paytirish.

$$x=\frac{1±1}{192}$$

x=\frac{1±1}{192} tenglamasini yeching, bunda ± musbat. 1 ni 1 ga qo'shish.

$$x=\frac{2}{192}$$

\frac{2}{192} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{1}{96}$$

x=\frac{1±1}{192} tenglamasini yeching, bunda ± manfiy. 1 dan 1 ni ayirish.

$$x=\frac{0}{192}$$

0 ni 192 ga bo'lish.

$$x=0$$

Tenglama yechildi.

$$x=\frac{1}{96} x=0$$

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.

$$96x^{2}-x=0$$

Ikki tarafini 96 ga bo‘ling.

$$\frac{96x^{2}-x}{96}=\frac{0}{96}$$

96 ga bo'lish 96 ga ko'paytirishni bekor qiladi.

$$x^{2}-\frac{1}{96}x=\frac{0}{96}$$

0 ni 96 ga bo'lish.

$$x^{2}-\frac{1}{96}x=0$$

-\frac{1}{96} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{1}{192} olish uchun. Keyin, -\frac{1}{192} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{1}{96}x+\left(-\frac{1}{192}\right)^{2}=\left(-\frac{1}{192}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{1}{192} kvadratini chiqarish.

$$x^{2}-\frac{1}{96}x+\frac{1}{36864}=\frac{1}{36864}$$

x^{2}-\frac{1}{96}x+\frac{1}{36864} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{1}{192}\right)^{2}=\frac{1}{36864}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{1}{192}\right)^{2}}=\sqrt{\frac{1}{36864}}$$

Qisqartirish.

$$x-\frac{1}{192}=\frac{1}{192} x-\frac{1}{192}=-\frac{1}{192}$$

\frac{1}{192} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{1}{96} x=0$$