6u^2-24u=0 eching

$$6 u ^ { 2 } - 24 u = 0$$

u uchun yechish

$$u=4$$

$$u=0$$

Faktorlash qadamlari

u omili.

$$u\left(6u-24\right)=0$$

Tenglamani yechish uchun u=0 va 6u-24=0 ni yeching.

$$u=0 u=4$$

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.

$$6u^{2}-24u=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 6 ni a, -24 ni b va 0 ni c bilan almashtiring.

$$u=\frac{-\left(-24\right)±\sqrt{\left(-24\right)^{2}}}{2\times 6}$$

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

$$u=\frac{-\left(-24\right)±24}{2\times 6}$$

-24 ning teskarisi 24 ga teng.

$$u=\frac{24±24}{2\times 6}$$

2 ni 6 marotabaga ko'paytirish.

$$u=\frac{24±24}{12}$$

u=\frac{24±24}{12} tenglamasini yeching, bunda ± musbat. 24 ni 24 ga qo'shish.

$$u=\frac{48}{12}$$

48 ni 12 ga bo'lish.

$$u=4$$

u=\frac{24±24}{12} tenglamasini yeching, bunda ± manfiy. 24 dan 24 ni ayirish.

$$u=\frac{0}{12}$$

0 ni 12 ga bo'lish.

$$u=0$$

Tenglama yechildi.

$$u=4 u=0$$

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.

$$6u^{2}-24u=0$$

Ikki tarafini 6 ga bo‘ling.

$$\frac{6u^{2}-24u}{6}=\frac{0}{6}$$

6 ga bo'lish 6 ga ko'paytirishni bekor qiladi.

$$u^{2}+\left(-\frac{24}{6}\right)u=\frac{0}{6}$$

-24 ni 6 ga bo'lish.

$$u^{2}-4u=\frac{0}{6}$$

0 ni 6 ga bo'lish.

$$u^{2}-4u=0$$

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

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

-2 kvadratini chiqarish.

$$u^{2}-4u+4=4$$

u^{2}-4u+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.

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

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

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

Qisqartirish.

$$u-2=2 u-2=-2$$

2 ni tenglamaning ikkala tarafiga qo'shish.

$$u=4 u=0$$