16x^2+64x+65=0 eching

$$16 x ^ { 2 } + 64 x + 65 = 0$$

x uchun yechish (complex solution)

$$x=-2+\frac{1}{4}i=-2+0,25i$$

$$x=-2-\frac{1}{4}i=-2-0,25i$$

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.

$$16x^{2}+64x+65=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 16 ni a, 64 ni b va 65 ni c bilan almashtiring.

$$x=\frac{-64±\sqrt{64^{2}-4\times 16\times 65}}{2\times 16}$$

64 kvadratini chiqarish.

$$x=\frac{-64±\sqrt{4096-4\times 16\times 65}}{2\times 16}$$

-4 ni 16 marotabaga ko'paytirish.

$$x=\frac{-64±\sqrt{4096-64\times 65}}{2\times 16}$$

-64 ni 65 marotabaga ko'paytirish.

$$x=\frac{-64±\sqrt{4096-4160}}{2\times 16}$$

4096 ni -4160 ga qo'shish.

$$x=\frac{-64±\sqrt{-64}}{2\times 16}$$

-64 ning kvadrat ildizini chiqarish.

$$x=\frac{-64±8i}{2\times 16}$$

2 ni 16 marotabaga ko'paytirish.

$$x=\frac{-64±8i}{32}$$

x=\frac{-64±8i}{32} tenglamasini yeching, bunda ± musbat. -64 ni 8i ga qo'shish.

$$x=\frac{-64+8i}{32}$$

-64+8i ni 32 ga bo'lish.

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

x=\frac{-64±8i}{32} tenglamasini yeching, bunda ± manfiy. -64 dan 8i ni ayirish.

$$x=\frac{-64-8i}{32}$$

-64-8i ni 32 ga bo'lish.

$$x=-2-\frac{1}{4}i$$

Tenglama yechildi.

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

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.

$$16x^{2}+64x+65=0$$

Tenglamaning ikkala tarafidan 65 ni ayirish.

$$16x^{2}+64x+65-65=-65$$

O‘zidan 65 ayirilsa 0 qoladi.

$$16x^{2}+64x=-65$$

Ikki tarafini 16 ga bo‘ling.

$$\frac{16x^{2}+64x}{16}=-\frac{65}{16}$$

16 ga bo'lish 16 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{64}{16}x=-\frac{65}{16}$$

64 ni 16 ga bo'lish.

$$x^{2}+4x=-\frac{65}{16}$$

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.

$$x^{2}+4x+2^{2}=-\frac{65}{16}+2^{2}$$

2 kvadratini chiqarish.

$$x^{2}+4x+4=-\frac{65}{16}+4$$

-\frac{65}{16} ni 4 ga qo'shish.

$$x^{2}+4x+4=-\frac{1}{16}$$

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.

$$\left(x+2\right)^{2}=-\frac{1}{16}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

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

Qisqartirish.

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

Tenglamaning ikkala tarafidan 2 ni ayirish.

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