2x^2-50=0 eching

$$2 x ^ { 2 } - 50 = 0$$

x uchun yechish

$$x=5$$

$$x=-5$$

Kvadratlar farqidan foydalangan qadamlar

Ikki tarafini 2 ga bo‘ling.

$$x^{2}-25=0$$

Hisoblang: x^{2}-25. x^{2}-25 ni x^{2}-5^{2} sifatida qaytadan yozish. Kvadratlarning farqini ushbu formula bilan hisoblash mumkin: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-5\right)\left(x+5\right)=0$$

Tenglamani yechish uchun x-5=0 va x+5=0 ni yeching.

$$x=5 x=-5$$

Kvadrat ildizini topish bo'yicha qadamlar

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

$$2x^{2}=50$$

Ikki tarafini 2 ga bo‘ling.

$$x^{2}=\frac{50}{2}$$

25 ni olish uchun 50 ni 2 ga bo‘ling.

$$x^{2}=25$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=5 x=-5$$

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.

$$2x^{2}-50=0$$

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 -50 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-50\right)}}{2\times 2}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 2\left(-50\right)}}{2\times 2}$$

-4 ni 2 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-8\left(-50\right)}}{2\times 2}$$

-8 ni -50 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{400}}{2\times 2}$$

400 ning kvadrat ildizini chiqarish.

$$x=\frac{0±20}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$x=\frac{0±20}{4}$$

x=\frac{0±20}{4} tenglamasini yeching, bunda ± musbat. 20 ni 4 ga bo'lish.

$$x=5$$

x=\frac{0±20}{4} tenglamasini yeching, bunda ± manfiy. -20 ni 4 ga bo'lish.

$$x=-5$$

Tenglama yechildi.

$$x=5 x=-5$$