2w^2-18=0 eching

$$2 { w }^{ 2 } -18=0$$

w uchun yechish

$$w=3$$

$$w=-3$$

Kvadratlar farqidan foydalangan qadamlar

Ikki tarafini 2 ga bo‘ling.

$$w^{2}-9=0$$

Hisoblang: w^{2}-9. w^{2}-9 ni w^{2}-3^{2} sifatida qaytadan yozish. Kvadratlarning farqini ushbu formula bilan hisoblash mumkin: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(w-3\right)\left(w+3\right)=0$$

Tenglamani yechish uchun w-3=0 va w+3=0 ni yeching.

$$w=3 w=-3$$

Kvadrat ildizini topish bo'yicha qadamlar

18 ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$2w^{2}=18$$

Ikki tarafini 2 ga bo‘ling.

$$w^{2}=\frac{18}{2}$$

9 ni olish uchun 18 ni 2 ga bo‘ling.

$$w^{2}=9$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$w=3 w=-3$$

Kvadrat tenglamalaridan foydalanish qoidalari

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.

$$2w^{2}-18=0$$

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 -18 ni c bilan almashtiring.

$$w=\frac{0±\sqrt{0^{2}-4\times 2\left(-18\right)}}{2\times 2}$$

0 kvadratini chiqarish.

$$w=\frac{0±\sqrt{-4\times 2\left(-18\right)}}{2\times 2}$$

-4 ni 2 marotabaga ko'paytirish.

$$w=\frac{0±\sqrt{-8\left(-18\right)}}{2\times 2}$$

-8 ni -18 marotabaga ko'paytirish.

$$w=\frac{0±\sqrt{144}}{2\times 2}$$

144 ning kvadrat ildizini chiqarish.

$$w=\frac{0±12}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$w=\frac{0±12}{4}$$

w=\frac{0±12}{4} tenglamasini yeching, bunda ± musbat. 12 ni 4 ga bo'lish.

$$w=3$$

w=\frac{0±12}{4} tenglamasini yeching, bunda ± manfiy. -12 ni 4 ga bo'lish.

$$w=-3$$

Tenglama yechildi.

$$w=3 w=-3$$