(-4x-3)-x^2-3=0 eching

$$(-4x-3)- { x }^{ 2 } -3=0$$

x uchun yechish (complex solution)

$$x=-\sqrt{2}i-2\approx -2-1,414213562i$$

$$x=-2+\sqrt{2}i\approx -2+1,414213562i$$

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.

$$-x^{2}-4x-6=0$$

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 -6 ni c bilan almashtiring.

$$x=\frac{-\left(-4\right)±\sqrt{\left(-4\right)^{2}-4\left(-1\right)\left(-6\right)}}{2\left(-1\right)}$$

-4 kvadratini chiqarish.

$$x=\frac{-\left(-4\right)±\sqrt{16-4\left(-1\right)\left(-6\right)}}{2\left(-1\right)}$$

-4 ni -1 marotabaga ko'paytirish.

$$x=\frac{-\left(-4\right)±\sqrt{16+4\left(-6\right)}}{2\left(-1\right)}$$

4 ni -6 marotabaga ko'paytirish.

$$x=\frac{-\left(-4\right)±\sqrt{16-24}}{2\left(-1\right)}$$

16 ni -24 ga qo'shish.

$$x=\frac{-\left(-4\right)±\sqrt{-8}}{2\left(-1\right)}$$

-8 ning kvadrat ildizini chiqarish.

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

-4 ning teskarisi 4 ga teng.

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

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{4±2\sqrt{2}i}{-2}$$

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

$$x=\frac{4+2\sqrt{2}i}{-2}$$

4+2i\sqrt{2} ni -2 ga bo'lish.

$$x=-\sqrt{2}i-2$$

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

$$x=\frac{-2\sqrt{2}i+4}{-2}$$

4-2i\sqrt{2} ni -2 ga bo'lish.

$$x=-2+\sqrt{2}i$$

Tenglama yechildi.

$$x=-\sqrt{2}i-2 x=-2+\sqrt{2}i$$

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.

$$-x^{2}-4x-6=0$$

6 ni tenglamaning ikkala tarafiga qo'shish.

$$-x^{2}-4x-6-\left(-6\right)=-\left(-6\right)$$

O‘zidan -6 ayirilsa 0 qoladi.

$$-x^{2}-4x=-\left(-6\right)$$

0 dan -6 ni ayirish.

$$-x^{2}-4x=6$$

Ikki tarafini -1 ga bo‘ling.

$$\frac{-x^{2}-4x}{-1}=\frac{6}{-1}$$

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

$$x^{2}+\left(-\frac{4}{-1}\right)x=\frac{6}{-1}$$

-4 ni -1 ga bo'lish.

$$x^{2}+4x=\frac{6}{-1}$$

6 ni -1 ga bo'lish.

$$x^{2}+4x=-6$$

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.

$$x^{2}+4x+2^{2}=-6+2^{2}$$

2 kvadratini chiqarish.

$$x^{2}+4x+4=-6+4$$

-6 ni 4 ga qo'shish.

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

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.

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

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

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

Qisqartirish.

$$x+2=\sqrt{2}i x+2=-\sqrt{2}i$$

Tenglamaning ikkala tarafidan 2 ni ayirish.

$$x=-2+\sqrt{2}i x=-\sqrt{2}i-2$$