left(4xright)^2+4x+4=0 eching

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

x uchun yechish (complex solution)

$$x=\frac{-1+\sqrt{15}i}{8}\approx -0,125+0,484122918i$$

$$x=\frac{-\sqrt{15}i-1}{8}\approx -0,125-0,484122918i$$

Kvadrat tenglamalaridan foydalanish qoidalari

\left(4x\right)^{2} ni kengaytirish.

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

2 daraja ko‘rsatkichini 4 ga hisoblang va 16 ni qiymatni oling.

$$16x^{2}+4x+4=0$$

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

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

4 kvadratini chiqarish.

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

-4 ni 16 marotabaga ko'paytirish.

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

-64 ni 4 marotabaga ko'paytirish.

$$x=\frac{-4±\sqrt{16-256}}{2\times 16}$$

16 ni -256 ga qo'shish.

$$x=\frac{-4±\sqrt{-240}}{2\times 16}$$

-240 ning kvadrat ildizini chiqarish.

$$x=\frac{-4±4\sqrt{15}i}{2\times 16}$$

2 ni 16 marotabaga ko'paytirish.

$$x=\frac{-4±4\sqrt{15}i}{32}$$

x=\frac{-4±4\sqrt{15}i}{32} tenglamasini yeching, bunda ± musbat. -4 ni 4i\sqrt{15} ga qo'shish.

$$x=\frac{-4+4\sqrt{15}i}{32}$$

-4+4i\sqrt{15} ni 32 ga bo'lish.

$$x=\frac{-1+\sqrt{15}i}{8}$$

x=\frac{-4±4\sqrt{15}i}{32} tenglamasini yeching, bunda ± manfiy. -4 dan 4i\sqrt{15} ni ayirish.

$$x=\frac{-4\sqrt{15}i-4}{32}$$

-4-4i\sqrt{15} ni 32 ga bo'lish.

$$x=\frac{-\sqrt{15}i-1}{8}$$

Tenglama yechildi.

$$x=\frac{-1+\sqrt{15}i}{8} x=\frac{-\sqrt{15}i-1}{8}$$

Kvadratni yakunlash bo'yicha qadamlar

\left(4x\right)^{2} ni kengaytirish.

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

2 daraja ko‘rsatkichini 4 ga hisoblang va 16 ni qiymatni oling.

$$16x^{2}+4x+4=0$$

Ikkala tarafdan 4 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

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

Ikki tarafini 16 ga bo‘ling.

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

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

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

\frac{4}{16} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

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

\frac{-4}{16} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

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

\frac{1}{4} ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{1}{8} olish uchun. Keyin, \frac{1}{8} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

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

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{1}{8} kvadratini chiqarish.

$$x^{2}+\frac{1}{4}x+\frac{1}{64}=-\frac{1}{4}+\frac{1}{64}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali -\frac{1}{4} ni \frac{1}{64} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}+\frac{1}{4}x+\frac{1}{64}=-\frac{15}{64}$$

x^{2}+\frac{1}{4}x+\frac{1}{64} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+\frac{1}{8}\right)^{2}=-\frac{15}{64}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{1}{8}\right)^{2}}=\sqrt{-\frac{15}{64}}$$

Qisqartirish.

$$x+\frac{1}{8}=\frac{\sqrt{15}i}{8} x+\frac{1}{8}=-\frac{\sqrt{15}i}{8}$$

Tenglamaning ikkala tarafidan \frac{1}{8} ni ayirish.

$$x=\frac{-1+\sqrt{15}i}{8} x=\frac{-\sqrt{15}i-1}{8}$$