10x^2-40=0 eching

$$10 x ^ { 2 } - 40 = 0$$

x uchun yechish

$$x=2$$

$$x=-2$$

Kvadratlar farqidan foydalangan qadamlar

Ikki tarafini 10 ga bo‘ling.

$$x^{2}-4=0$$

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

$$\left(x-2\right)\left(x+2\right)=0$$

Tenglamani yechish uchun x-2=0 va x+2=0 ni yeching.

$$x=2 x=-2$$

Kvadrat ildizini topish bo'yicha qadamlar

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

$$10x^{2}=40$$

Ikki tarafini 10 ga bo‘ling.

$$x^{2}=\frac{40}{10}$$

4 ni olish uchun 40 ni 10 ga bo‘ling.

$$x^{2}=4$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=2 x=-2$$

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.

$$10x^{2}-40=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 10 ni a, 0 ni b va -40 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 10\left(-40\right)}}{2\times 10}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 10\left(-40\right)}}{2\times 10}$$

-4 ni 10 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-40\left(-40\right)}}{2\times 10}$$

-40 ni -40 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{1600}}{2\times 10}$$

1600 ning kvadrat ildizini chiqarish.

$$x=\frac{0±40}{2\times 10}$$

2 ni 10 marotabaga ko'paytirish.

$$x=\frac{0±40}{20}$$

x=\frac{0±40}{20} tenglamasini yeching, bunda ± musbat. 40 ni 20 ga bo'lish.

$$x=2$$

x=\frac{0±40}{20} tenglamasini yeching, bunda ± manfiy. -40 ni 20 ga bo'lish.

$$x=-2$$

Tenglama yechildi.

$$x=2 x=-2$$