2x-3x^2-4x+2x^2-3=7 eching

$$2 x - 3 x ^ { 2 } - 4 x + 2 x ^ { 2 } - 3 = 7$$

x uchun yechish (complex solution)

$$x=-1-3i$$

$$x=-1+3i$$

Kvadrat tenglamalaridan foydalanish qoidalari

-2x ni olish uchun 2x va -4x ni birlashtirish.

$$-2x-3x^{2}+2x^{2}-3=7$$

-x^{2} ni olish uchun -3x^{2} va 2x^{2} ni birlashtirish.

$$-2x-x^{2}-3=7$$

Ikkala tarafdan 7 ni ayirish.

$$-2x-x^{2}-3-7=0$$

-10 olish uchun -3 dan 7 ni ayirish.

$$-2x-x^{2}-10=0$$

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.

$$-x^{2}-2x-10=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -1 ni a, -2 ni b va -10 ni c bilan almashtiring.

$$x=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\left(-1\right)\left(-10\right)}}{2\left(-1\right)}$$

-2 kvadratini chiqarish.

$$x=\frac{-\left(-2\right)±\sqrt{4-4\left(-1\right)\left(-10\right)}}{2\left(-1\right)}$$

-4 ni -1 marotabaga ko'paytirish.

$$x=\frac{-\left(-2\right)±\sqrt{4+4\left(-10\right)}}{2\left(-1\right)}$$

4 ni -10 marotabaga ko'paytirish.

$$x=\frac{-\left(-2\right)±\sqrt{4-40}}{2\left(-1\right)}$$

4 ni -40 ga qo'shish.

$$x=\frac{-\left(-2\right)±\sqrt{-36}}{2\left(-1\right)}$$

-36 ning kvadrat ildizini chiqarish.

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

-2 ning teskarisi 2 ga teng.

$$x=\frac{2±6i}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{2±6i}{-2}$$

x=\frac{2±6i}{-2} tenglamasini yeching, bunda ± musbat. 2 ni 6i ga qo'shish.

$$x=\frac{2+6i}{-2}$$

2+6i ni -2 ga bo'lish.

$$x=-1-3i$$

x=\frac{2±6i}{-2} tenglamasini yeching, bunda ± manfiy. 2 dan 6i ni ayirish.

$$x=\frac{2-6i}{-2}$$

2-6i ni -2 ga bo'lish.

$$x=-1+3i$$

Tenglama yechildi.

$$x=-1-3i x=-1+3i$$

Kvadratni yakunlash bo'yicha qadamlar

-2x ni olish uchun 2x va -4x ni birlashtirish.

$$-2x-3x^{2}+2x^{2}-3=7$$

-x^{2} ni olish uchun -3x^{2} va 2x^{2} ni birlashtirish.

$$-2x-x^{2}-3=7$$

3 ni ikki tarafga qo’shing.

$$-2x-x^{2}=7+3$$

10 olish uchun 7 va 3'ni qo'shing.

$$-2x-x^{2}=10$$

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

$$-x^{2}-2x=10$$

Ikki tarafini -1 ga bo‘ling.

$$\frac{-x^{2}-2x}{-1}=\frac{10}{-1}$$

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

$$x^{2}+\left(-\frac{2}{-1}\right)x=\frac{10}{-1}$$

-2 ni -1 ga bo'lish.

$$x^{2}+2x=\frac{10}{-1}$$

10 ni -1 ga bo'lish.

$$x^{2}+2x=-10$$

2 ni bo‘lish, x shartining koeffitsienti, 2 ga 1 olish uchun. Keyin, 1 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+2x+1^{2}=-10+1^{2}$$

1 kvadratini chiqarish.

$$x^{2}+2x+1=-10+1$$

-10 ni 1 ga qo'shish.

$$x^{2}+2x+1=-9$$

x^{2}+2x+1 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+1\right)^{2}=-9$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+1\right)^{2}}=\sqrt{-9}$$

Qisqartirish.

$$x+1=3i x+1=-3i$$

Tenglamaning ikkala tarafidan 1 ni ayirish.

$$x=-1+3i x=-1-3i$$