8x+2-3x^2+1=35-x^2 eching

$$8 x + 2 - 3 x ^ { 2 } + 1 = 35 - x ^ { 2 }$$

x uchun yechish (complex solution)

$$x=2+2\sqrt{3}i\approx 2+3,464101615i$$

$$x=-2\sqrt{3}i+2\approx 2-3,464101615i$$

Kvadrat tenglamalaridan foydalanish qoidalari

3 olish uchun 2 va 1'ni qo'shing.

$$8x+3-3x^{2}=35-x^{2}$$

Ikkala tarafdan 35 ni ayirish.

$$8x+3-3x^{2}-35=-x^{2}$$

-32 olish uchun 3 dan 35 ni ayirish.

$$8x-32-3x^{2}=-x^{2}$$

x^{2} ni ikki tarafga qo’shing.

$$8x-32-3x^{2}+x^{2}=0$$

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

$$8x-32-2x^{2}=0$$

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.

$$-2x^{2}+8x-32=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -2 ni a, 8 ni b va -32 ni c bilan almashtiring.

$$x=\frac{-8±\sqrt{8^{2}-4\left(-2\right)\left(-32\right)}}{2\left(-2\right)}$$

8 kvadratini chiqarish.

$$x=\frac{-8±\sqrt{64-4\left(-2\right)\left(-32\right)}}{2\left(-2\right)}$$

-4 ni -2 marotabaga ko'paytirish.

$$x=\frac{-8±\sqrt{64+8\left(-32\right)}}{2\left(-2\right)}$$

8 ni -32 marotabaga ko'paytirish.

$$x=\frac{-8±\sqrt{64-256}}{2\left(-2\right)}$$

64 ni -256 ga qo'shish.

$$x=\frac{-8±\sqrt{-192}}{2\left(-2\right)}$$

-192 ning kvadrat ildizini chiqarish.

$$x=\frac{-8±8\sqrt{3}i}{2\left(-2\right)}$$

2 ni -2 marotabaga ko'paytirish.

$$x=\frac{-8±8\sqrt{3}i}{-4}$$

x=\frac{-8±8\sqrt{3}i}{-4} tenglamasini yeching, bunda ± musbat. -8 ni 8i\sqrt{3} ga qo'shish.

$$x=\frac{-8+8\sqrt{3}i}{-4}$$

-8+8i\sqrt{3} ni -4 ga bo'lish.

$$x=-2\sqrt{3}i+2$$

x=\frac{-8±8\sqrt{3}i}{-4} tenglamasini yeching, bunda ± manfiy. -8 dan 8i\sqrt{3} ni ayirish.

$$x=\frac{-8\sqrt{3}i-8}{-4}$$

-8-8i\sqrt{3} ni -4 ga bo'lish.

$$x=2+2\sqrt{3}i$$

Tenglama yechildi.

$$x=-2\sqrt{3}i+2 x=2+2\sqrt{3}i$$

Kvadratni yakunlash bo'yicha qadamlar

3 olish uchun 2 va 1'ni qo'shing.

$$8x+3-3x^{2}=35-x^{2}$$

x^{2} ni ikki tarafga qo’shing.

$$8x+3-3x^{2}+x^{2}=35$$

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

$$8x+3-2x^{2}=35$$

Ikkala tarafdan 3 ni ayirish.

$$8x-2x^{2}=35-3$$

32 olish uchun 35 dan 3 ni ayirish.

$$8x-2x^{2}=32$$

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

$$-2x^{2}+8x=32$$

Ikki tarafini -2 ga bo‘ling.

$$\frac{-2x^{2}+8x}{-2}=\frac{32}{-2}$$

-2 ga bo'lish -2 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{8}{-2}x=\frac{32}{-2}$$

8 ni -2 ga bo'lish.

$$x^{2}-4x=\frac{32}{-2}$$

32 ni -2 ga bo'lish.

$$x^{2}-4x=-16$$

-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.

$$x^{2}-4x+\left(-2\right)^{2}=-16+\left(-2\right)^{2}$$

-2 kvadratini chiqarish.

$$x^{2}-4x+4=-16+4$$

-16 ni 4 ga qo'shish.

$$x^{2}-4x+4=-12$$

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.

$$\left(x-2\right)^{2}=-12$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-2\right)^{2}}=\sqrt{-12}$$

Qisqartirish.

$$x-2=2\sqrt{3}i x-2=-2\sqrt{3}i$$

2 ni tenglamaning ikkala tarafiga qo'shish.

$$x=2+2\sqrt{3}i x=-2\sqrt{3}i+2$$