-4x^2=1/4 eching

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

x uchun yechish (complex solution)

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

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

Kvadrat ildizini topish bo'yicha qadamlar

Ikki tarafini -4 ga bo‘ling.

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

\frac{\frac{1}{4}}{-4} ni yagona kasrga aylantiring.

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

-16 hosil qilish uchun 4 va -4 ni ko'paytirish.

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

\frac{1}{-16} kasri manfiy belgini olib tashlash bilan -\frac{1}{16} sifatida qayta yozilishi mumkin.

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

Tenglama yechildi.

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

Kvadrat tenglamalaridan foydalanish qoidalari

Ikki tarafini -4 ga bo‘ling.

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

\frac{\frac{1}{4}}{-4} ni yagona kasrga aylantiring.

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

-16 hosil qilish uchun 4 va -4 ni ko'paytirish.

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

\frac{1}{-16} kasri manfiy belgini olib tashlash bilan -\frac{1}{16} sifatida qayta yozilishi mumkin.

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

\frac{1}{16} ni ikki tarafga qo’shing.

$$x^{2}+\frac{1}{16}=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 0 ni b va \frac{1}{16} ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{1}{16}}}{2}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times \frac{1}{16}}}{2}$$

-4 ni \frac{1}{16} marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-\frac{1}{4}}}{2}$$

-\frac{1}{4} ning kvadrat ildizini chiqarish.

$$x=\frac{0±\frac{1}{2}i}{2}$$

x=\frac{0±\frac{1}{2}i}{2} tenglamasini yeching, bunda ± musbat.

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

x=\frac{0±\frac{1}{2}i}{2} tenglamasini yeching, bunda ± manfiy.

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

Tenglama yechildi.

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