12x^2-9x=0 eching

$$12 x ^ { 2 } - 9 x = 0$$

x uchun yechish

$$x=\frac{3}{4}=0,75$$

$$x=0$$

Faktorlash qadamlari

x omili.

$$x\left(12x-9\right)=0$$

Tenglamani yechish uchun x=0 va 12x-9=0 ni yeching.

$$x=0 x=\frac{3}{4}$$

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.

$$12x^{2}-9x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 12 ni a, -9 ni b va 0 ni c bilan almashtiring.

$$x=\frac{-\left(-9\right)±\sqrt{\left(-9\right)^{2}}}{2\times 12}$$

\left(-9\right)^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-9\right)±9}{2\times 12}$$

-9 ning teskarisi 9 ga teng.

$$x=\frac{9±9}{2\times 12}$$

2 ni 12 marotabaga ko'paytirish.

$$x=\frac{9±9}{24}$$

x=\frac{9±9}{24} tenglamasini yeching, bunda ± musbat. 9 ni 9 ga qo'shish.

$$x=\frac{18}{24}$$

\frac{18}{24} ulushini 6 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{3}{4}$$

x=\frac{9±9}{24} tenglamasini yeching, bunda ± manfiy. 9 dan 9 ni ayirish.

$$x=\frac{0}{24}$$

0 ni 24 ga bo'lish.

$$x=0$$

Tenglama yechildi.

$$x=\frac{3}{4} x=0$$

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.

$$12x^{2}-9x=0$$

Ikki tarafini 12 ga bo‘ling.

$$\frac{12x^{2}-9x}{12}=\frac{0}{12}$$

12 ga bo'lish 12 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{9}{12}\right)x=\frac{0}{12}$$

\frac{-9}{12} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}-\frac{3}{4}x=\frac{0}{12}$$

0 ni 12 ga bo'lish.

$$x^{2}-\frac{3}{4}x=0$$

-\frac{3}{4} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{3}{8} olish uchun. Keyin, -\frac{3}{8} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{3}{4}x+\left(-\frac{3}{8}\right)^{2}=\left(-\frac{3}{8}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{3}{8} kvadratini chiqarish.

$$x^{2}-\frac{3}{4}x+\frac{9}{64}=\frac{9}{64}$$

x^{2}-\frac{3}{4}x+\frac{9}{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.

$$\left(x-\frac{3}{8}\right)^{2}=\frac{9}{64}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{3}{8}\right)^{2}}=\sqrt{\frac{9}{64}}$$

Qisqartirish.

$$x-\frac{3}{8}=\frac{3}{8} x-\frac{3}{8}=-\frac{3}{8}$$

\frac{3}{8} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{3}{4} x=0$$