-3x^2-24x-13=-13 eching

$$- 3 x ^ { 2 } - 24 x - 13 = - 13$$

x uchun yechish

$$x=-8$$

$$x=0$$

Faktorlash qadamlari

13 ni ikki tarafga qo’shing.

$$-3x^{2}-24x-13+13=0$$

0 olish uchun -13 va 13'ni qo'shing.

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

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.

$$-3x^{2}-24x-13=-13$$

13 ni tenglamaning ikkala tarafiga qo'shish.

$$-3x^{2}-24x-13-\left(-13\right)=-13-\left(-13\right)$$

O‘zidan -13 ayirilsa 0 qoladi.

$$-3x^{2}-24x-13-\left(-13\right)=0$$

-13 dan -13 ni ayirish.

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

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.

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

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

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

-24 ning teskarisi 24 ga teng.

$$x=\frac{24±24}{2\left(-3\right)}$$

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.

$$-3x^{2}-24x-13=-13$$

13 ni tenglamaning ikkala tarafiga qo'shish.

$$-3x^{2}-24x-13-\left(-13\right)=-13-\left(-13\right)$$

O‘zidan -13 ayirilsa 0 qoladi.

$$-3x^{2}-24x=-13-\left(-13\right)$$

-13 dan -13 ni ayirish.

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

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.

$$x^{2}+8x+4^{2}=4^{2}$$

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.

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

Tenglamaning ikkala tarafidan 4 ni ayirish.

$$x=0 x=-8$$