4x^2-12x=0 eching

$$4 x ^ { 2 } - 12 x = 0$$

x uchun yechish

$$x=3$$

$$x=0$$

Faktorlash qadamlari

x omili.

$$x\left(4x-12\right)=0$$

Tenglamani yechish uchun x=0 va 4x-12=0 ni yeching.

$$x=0 x=3$$

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.

$$4x^{2}-12x=0$$

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

$$x=\frac{-\left(-12\right)±\sqrt{\left(-12\right)^{2}}}{2\times 4}$$

\left(-12\right)^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-12\right)±12}{2\times 4}$$

-12 ning teskarisi 12 ga teng.

$$x=\frac{12±12}{2\times 4}$$

2 ni 4 marotabaga ko'paytirish.

$$x=\frac{12±12}{8}$$

x=\frac{12±12}{8} tenglamasini yeching, bunda ± musbat. 12 ni 12 ga qo'shish.

$$x=\frac{24}{8}$$

24 ni 8 ga bo'lish.

$$x=3$$

x=\frac{12±12}{8} tenglamasini yeching, bunda ± manfiy. 12 dan 12 ni ayirish.

$$x=\frac{0}{8}$$

0 ni 8 ga bo'lish.

$$x=0$$

Tenglama yechildi.

$$x=3 x=0$$

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.

$$4x^{2}-12x=0$$

Ikki tarafini 4 ga bo‘ling.

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

4 ga bo'lish 4 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{12}{4}\right)x=\frac{0}{4}$$

-12 ni 4 ga bo'lish.

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

0 ni 4 ga bo'lish.

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

-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.

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

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

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

x^{2}-3x+\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.

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

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

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

Qisqartirish.

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

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

$$x=3 x=0$$