2x^2=x-4 eching

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

x uchun yechish (complex solution)

$$x=\frac{1+\sqrt{31}i}{4}\approx 0,25+1,391941091i$$

$$x=\frac{-\sqrt{31}i+1}{4}\approx 0,25-1,391941091i$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan x ni ayirish.

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

4 ni ikki tarafga qo’shing.

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

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

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

-4 ni 2 marotabaga ko'paytirish.

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

-8 ni 4 marotabaga ko'paytirish.

$$x=\frac{-\left(-1\right)±\sqrt{1-32}}{2\times 2}$$

1 ni -32 ga qo'shish.

$$x=\frac{-\left(-1\right)±\sqrt{-31}}{2\times 2}$$

-31 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-1\right)±\sqrt{31}i}{2\times 2}$$

-1 ning teskarisi 1 ga teng.

$$x=\frac{1±\sqrt{31}i}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$x=\frac{1±\sqrt{31}i}{4}$$

x=\frac{1±\sqrt{31}i}{4} tenglamasini yeching, bunda ± musbat. 1 ni i\sqrt{31} ga qo'shish.

$$x=\frac{1+\sqrt{31}i}{4}$$

x=\frac{1±\sqrt{31}i}{4} tenglamasini yeching, bunda ± manfiy. 1 dan i\sqrt{31} ni ayirish.

$$x=\frac{-\sqrt{31}i+1}{4}$$

Tenglama yechildi.

$$x=\frac{1+\sqrt{31}i}{4} x=\frac{-\sqrt{31}i+1}{4}$$

Kvadratni yakunlash bo'yicha qadamlar

Ikkala tarafdan x ni ayirish.

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

Ikki tarafini 2 ga bo‘ling.

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

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

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

-4 ni 2 ga bo'lish.

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

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

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

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{1}{4} kvadratini chiqarish.

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

-2 ni \frac{1}{16} ga qo'shish.

$$x^{2}-\frac{1}{2}x+\frac{1}{16}=-\frac{31}{16}$$

x^{2}-\frac{1}{2}x+\frac{1}{16} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{1}{4}\right)^{2}=-\frac{31}{16}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{1}{4}\right)^{2}}=\sqrt{-\frac{31}{16}}$$

Qisqartirish.

$$x-\frac{1}{4}=\frac{\sqrt{31}i}{4} x-\frac{1}{4}=-\frac{\sqrt{31}i}{4}$$

\frac{1}{4} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{1+\sqrt{31}i}{4} x=\frac{-\sqrt{31}i+1}{4}$$