-1-2x^2=-2 eching

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

x uchun yechish

$$x=\frac{\sqrt{2}}{2}\approx 0,707106781$$

$$x=-\frac{\sqrt{2}}{2}\approx -0,707106781$$

Kvadrat ildizini topish bo'yicha qadamlar

1 ni ikki tarafga qo’shing.

$$-2x^{2}=-2+1$$

-1 olish uchun -2 va 1'ni qo'shing.

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

Ikki tarafini -2 ga bo‘ling.

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

Ikkala surat va maxrajdan manfiy belgini olib tashlash bilan \frac{-1}{-2} kasrini \frac{1}{2} ga soddalashtirish mumkin.

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

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

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

Kvadrat tenglamalaridan foydalanish qoidalari

2 ni ikki tarafga qo’shing.

$$-1-2x^{2}+2=0$$

1 olish uchun -1 va 2'ni qo'shing.

$$1-2x^{2}=0$$

Bu kabi kvadrat tenglamalarni x^{2} sharti bilan, biroq x shartisiz hamon kvadrat tenglamasidan foydalanib yechish mumkin, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, ular standart formulaga solingandan so'ng: ax^{2}+bx+c=0.

$$-2x^{2}+1=0$$

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

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

0 kvadratini chiqarish.

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

-4 ni -2 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{8}}{2\left(-2\right)}$$

8 ning kvadrat ildizini chiqarish.

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

2 ni -2 marotabaga ko'paytirish.

$$x=\frac{0±2\sqrt{2}}{-4}$$

x=\frac{0±2\sqrt{2}}{-4} tenglamasini yeching, bunda ± musbat.

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

x=\frac{0±2\sqrt{2}}{-4} tenglamasini yeching, bunda ± manfiy.

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

Tenglama yechildi.

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