2x^2-3=29 eching

$$2 x ^ { 2 } - 3 = 29$$

x uchun yechish

$$x=4$$

$$x=-4$$

Kvadratlar farqidan foydalangan qadamlar

Ikkala tarafdan 29 ni ayirish.

$$2x^{2}-3-29=0$$

-32 olish uchun -3 dan 29 ni ayirish.

$$2x^{2}-32=0$$

Ikki tarafini 2 ga bo‘ling.

$$x^{2}-16=0$$

Hisoblang: x^{2}-16. x^{2}-16 ni x^{2}-4^{2} sifatida qaytadan yozish. Kvadratlarning farqini ushbu formula bilan hisoblash mumkin: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-4\right)\left(x+4\right)=0$$

Tenglamani yechish uchun x-4=0 va x+4=0 ni yeching.

$$x=4 x=-4$$

Kvadrat ildizini topish bo'yicha qadamlar

3 ni ikki tarafga qo’shing.

$$2x^{2}=29+3$$

32 olish uchun 29 va 3'ni qo'shing.

$$2x^{2}=32$$

Ikki tarafini 2 ga bo‘ling.

$$x^{2}=\frac{32}{2}$$

16 ni olish uchun 32 ni 2 ga bo‘ling.

$$x^{2}=16$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=4 x=-4$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 29 ni ayirish.

$$2x^{2}-3-29=0$$

-32 olish uchun -3 dan 29 ni ayirish.

$$2x^{2}-32=0$$

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 -32 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-32\right)}}{2\times 2}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 2\left(-32\right)}}{2\times 2}$$

-4 ni 2 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-8\left(-32\right)}}{2\times 2}$$

-8 ni -32 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{256}}{2\times 2}$$

256 ning kvadrat ildizini chiqarish.

$$x=\frac{0±16}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$x=\frac{0±16}{4}$$

x=\frac{0±16}{4} tenglamasini yeching, bunda ± musbat. 16 ni 4 ga bo'lish.

$$x=4$$

x=\frac{0±16}{4} tenglamasini yeching, bunda ± manfiy. -16 ni 4 ga bo'lish.

$$x=-4$$

Tenglama yechildi.

$$x=4 x=-4$$