6x^2+24x=0 eching

$$6 x ^ { 2 } + 24 x = 0$$

x uchun yechish

$$x=-4$$

$$x=0$$

Faktorlash qadamlari

x omili.

$$x\left(6x+24\right)=0$$

Tenglamani yechish uchun x=0 va 6x+24=0 ni yeching.

$$x=0 x=-4$$

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.

$$6x^{2}+24x=0$$

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.

$$x=\frac{-24±\sqrt{24^{2}}}{2\times 6}$$

24^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-24±24}{2\times 6}$$

2 ni 6 marotabaga ko'paytirish.

$$x=\frac{-24±24}{12}$$

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

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

0 ni 12 ga bo'lish.

$$x=0$$

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

$$x=-\frac{48}{12}$$

-48 ni 12 ga bo'lish.

$$x=-4$$

Tenglama yechildi.

$$x=0 x=-4$$

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.

$$6x^{2}+24x=0$$

Ikki tarafini 6 ga bo‘ling.

$$\frac{6x^{2}+24x}{6}=\frac{0}{6}$$

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

$$x^{2}+\frac{24}{6}x=\frac{0}{6}$$

24 ni 6 ga bo'lish.

$$x^{2}+4x=\frac{0}{6}$$

0 ni 6 ga bo'lish.

$$x^{2}+4x=0$$

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.

$$x^{2}+4x+2^{2}=2^{2}$$

2 kvadratini chiqarish.

$$x^{2}+4x+4=4$$

x^{2}+4x+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.

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

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

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

Qisqartirish.

$$x+2=2 x+2=-2$$

Tenglamaning ikkala tarafidan 2 ni ayirish.

$$x=0 x=-4$$