3x^2=75 eching

$$3 x ^ { 2 } = 75$$

x uchun yechish

$$x=5$$

$$x=-5$$

Kvadratlar farqidan foydalangan qadamlar

Ikki tarafini 3 ga bo‘ling.

$$x^{2}=\frac{75}{3}$$

25 ni olish uchun 75 ni 3 ga bo‘ling.

$$x^{2}=25$$

Ikkala tarafdan 25 ni ayirish.

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

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

Ikki tarafini 3 ga bo‘ling.

$$x^{2}=\frac{75}{3}$$

25 ni olish uchun 75 ni 3 ga bo‘ling.

$$x^{2}=25$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=5 x=-5$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikki tarafini 3 ga bo‘ling.

$$x^{2}=\frac{75}{3}$$

25 ni olish uchun 75 ni 3 ga bo‘ling.

$$x^{2}=25$$

Ikkala tarafdan 25 ni ayirish.

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

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 0 ni b va -25 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\left(-25\right)}}{2}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\left(-25\right)}}{2}$$

-4 ni -25 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{100}}{2}$$

100 ning kvadrat ildizini chiqarish.

$$x=\frac{0±10}{2}$$

x=\frac{0±10}{2} tenglamasini yeching, bunda ± musbat. 10 ni 2 ga bo'lish.

$$x=5$$

x=\frac{0±10}{2} tenglamasini yeching, bunda ± manfiy. -10 ni 2 ga bo'lish.

$$x=-5$$

Tenglama yechildi.

$$x=5 x=-5$$