-x-x^2-3x+4-4=0 eching

$$- x - x ^ { 2 } - 3 x + 4 - 4 = 0$$

x uchun yechish

$$x=-4$$

$$x=0$$

Faktorlash qadamlari

0 olish uchun 4 dan 4 ni ayirish.

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

-4x ni olish uchun -x va -3x ni birlashtirish.

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

x omili.

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

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

$$x=0 x=-4$$

Kvadrat tenglamalaridan foydalanish qoidalari

0 olish uchun 4 dan 4 ni ayirish.

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

-4x ni olish uchun -x va -3x ni birlashtirish.

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

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.

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

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -1 ni a, -4 ni b va 0 ni c bilan almashtiring.

$$x=\frac{-\left(-4\right)±\sqrt{\left(-4\right)^{2}}}{2\left(-1\right)}$$

\left(-4\right)^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-4\right)±4}{2\left(-1\right)}$$

-4 ning teskarisi 4 ga teng.

$$x=\frac{4±4}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{4±4}{-2}$$

x=\frac{4±4}{-2} tenglamasini yeching, bunda ± musbat. 4 ni 4 ga qo'shish.

$$x=\frac{8}{-2}$$

8 ni -2 ga bo'lish.

$$x=-4$$

x=\frac{4±4}{-2} tenglamasini yeching, bunda ± manfiy. 4 dan 4 ni ayirish.

$$x=\frac{0}{-2}$$

0 ni -2 ga bo'lish.

$$x=0$$

Tenglama yechildi.

$$x=-4 x=0$$

Kvadratni yakunlash bo'yicha qadamlar

0 olish uchun 4 dan 4 ni ayirish.

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

-4x ni olish uchun -x va -3x ni birlashtirish.

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

Bu kabi kvadrat tenglamalarni kvadratni yakunlab yechish mumkin. Kvadratni yechish uchun tenglama avval ushbu shaklda bo'lishi shart: x^{2}+bx=c.

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

Ikki tarafini -1 ga bo‘ling.

$$\frac{-x^{2}-4x}{-1}=\frac{0}{-1}$$

-1 ga bo'lish -1 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{4}{-1}\right)x=\frac{0}{-1}$$

-4 ni -1 ga bo'lish.

$$x^{2}+4x=\frac{0}{-1}$$

0 ni -1 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.

$$x=0 x=-4$$