3x^2-24x=0 eching

$$3 x ^ { 2 } - 24 x = 0$$

x uchun yechish

$$x=8$$

$$x=0$$

Faktorlash qadamlari

x omili.

$$x\left(3x-24\right)=0$$

Tenglamani yechish uchun x=0 va 3x-24=0 ni yeching.

$$x=0 x=8$$

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.

$$3x^{2}-24x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 3 ni a, -24 ni b va 0 ni c bilan almashtiring.

$$x=\frac{-\left(-24\right)±\sqrt{\left(-24\right)^{2}}}{2\times 3}$$

\left(-24\right)^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-24\right)±24}{2\times 3}$$

-24 ning teskarisi 24 ga teng.

$$x=\frac{24±24}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$x=\frac{24±24}{6}$$

x=\frac{24±24}{6} tenglamasini yeching, bunda ± musbat. 24 ni 24 ga qo'shish.

$$x=\frac{48}{6}$$

48 ni 6 ga bo'lish.

$$x=8$$

x=\frac{24±24}{6} tenglamasini yeching, bunda ± manfiy. 24 dan 24 ni ayirish.

$$x=\frac{0}{6}$$

0 ni 6 ga bo'lish.

$$x=0$$

Tenglama yechildi.

$$x=8 x=0$$

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.

$$3x^{2}-24x=0$$

Ikki tarafini 3 ga bo‘ling.

$$\frac{3x^{2}-24x}{3}=\frac{0}{3}$$

3 ga bo'lish 3 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{24}{3}\right)x=\frac{0}{3}$$

-24 ni 3 ga bo'lish.

$$x^{2}-8x=\frac{0}{3}$$

0 ni 3 ga bo'lish.

$$x^{2}-8x=0$$

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

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

-4 kvadratini chiqarish.

$$x^{2}-8x+16=16$$

x^{2}-8x+16 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-4\right)^{2}=16$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-4\right)^{2}}=\sqrt{16}$$

Qisqartirish.

$$x-4=4 x-4=-4$$

4 ni tenglamaning ikkala tarafiga qo'shish.

$$x=8 x=0$$