1/2x^2-32=0 eching

$$\frac { 1 } { 2 } x ^ { 2 } - 32 = 0$$

x uchun yechish

$$x=8$$

$$x=-8$$

Kvadratlar farqidan foydalangan qadamlar

Ikkala tarafini 2 ga ko‘paytiring.

$$x^{2}-64=0$$

Hisoblang: x^{2}-64. x^{2}-64 ni x^{2}-8^{2} sifatida qaytadan yozish. Kvadratlarning farqini ushbu formula bilan hisoblash mumkin: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-8\right)\left(x+8\right)=0$$

Tenglamani yechish uchun x-8=0 va x+8=0 ni yeching.

$$x=8 x=-8$$

Kvadrat ildizini topish bo'yicha qadamlar

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

$$\frac{1}{2}x^{2}=32$$

Ikki tarafini 2 va teskari kasri \frac{1}{2} ga ko‘paytiring.

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

64 hosil qilish uchun 32 va 2 ni ko'paytirish.

$$x^{2}=64$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=8 x=-8$$

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.

$$\frac{1}{2}x^{2}-32=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} \frac{1}{2} ni a, 0 ni b va -32 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{1}{2}\left(-32\right)}}{2\times \frac{1}{2}}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times \frac{1}{2}\left(-32\right)}}{2\times \frac{1}{2}}$$

-4 ni \frac{1}{2} marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-2\left(-32\right)}}{2\times \frac{1}{2}}$$

-2 ni -32 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{64}}{2\times \frac{1}{2}}$$

64 ning kvadrat ildizini chiqarish.

$$x=\frac{0±8}{2\times \frac{1}{2}}$$

2 ni \frac{1}{2} marotabaga ko'paytirish.

$$x=\frac{0±8}{1}$$

x=\frac{0±8}{1} tenglamasini yeching, bunda ± musbat.

$$x=8$$

x=\frac{0±8}{1} tenglamasini yeching, bunda ± manfiy.

$$x=-8$$

Tenglama yechildi.

$$x=8 x=-8$$