4/2=-x^2+1/2/2 eching

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

x uchun yechish (complex solution)

$$x=-\frac{\sqrt{14}i}{2}\approx -0-1,870828693i$$

$$x=\frac{\sqrt{14}i}{2}\approx 1,870828693i$$

Kvadrat ildizini topish bo'yicha qadamlar

Tenglamaning ikkala tarafini 2 ga ko'paytirish.

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

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

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

Ikkala tarafdan \frac{1}{2} ni ayirish.

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

\frac{7}{2} olish uchun 4 dan \frac{1}{2} ni ayirish.

$$-x^{2}=\frac{7}{2}$$

Ikki tarafini -1 ga bo‘ling.

$$x^{2}=\frac{\frac{7}{2}}{-1}$$

\frac{\frac{7}{2}}{-1} ni yagona kasrga aylantiring.

$$x^{2}=\frac{7}{2\left(-1\right)}$$

-2 hosil qilish uchun 2 va -1 ni ko'paytirish.

$$x^{2}=\frac{7}{-2}$$

\frac{7}{-2} kasri manfiy belgini olib tashlash bilan -\frac{7}{2} sifatida qayta yozilishi mumkin.

$$x^{2}=-\frac{7}{2}$$

Tenglama yechildi.

$$x=\frac{\sqrt{14}i}{2} x=-\frac{\sqrt{14}i}{2}$$

Kvadrat tenglamalaridan foydalanish qoidalari

Tenglamaning ikkala tarafini 2 ga ko'paytirish.

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

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

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

Ikkala tarafdan 4 ni ayirish.

$$-x^{2}+\frac{1}{2}-4=0$$

-\frac{7}{2} olish uchun \frac{1}{2} dan 4 ni ayirish.

$$-x^{2}-\frac{7}{2}=0$$

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{7}{2} ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)\left(-\frac{7}{2}\right)}}{2\left(-1\right)}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\left(-1\right)\left(-\frac{7}{2}\right)}}{2\left(-1\right)}$$

-4 ni -1 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{4\left(-\frac{7}{2}\right)}}{2\left(-1\right)}$$

4 ni -\frac{7}{2} marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-14}}{2\left(-1\right)}$$

-14 ning kvadrat ildizini chiqarish.

$$x=\frac{0±\sqrt{14}i}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{14}i}{-2}$$

x=\frac{0±\sqrt{14}i}{-2} tenglamasini yeching, bunda ± musbat.

$$x=-\frac{\sqrt{14}i}{2}$$

x=\frac{0±\sqrt{14}i}{-2} tenglamasini yeching, bunda ± manfiy.

$$x=\frac{\sqrt{14}i}{2}$$

Tenglama yechildi.

$$x=-\frac{\sqrt{14}i}{2} x=\frac{\sqrt{14}i}{2}$$