3x^2+47x^2-7=0 eching

$$3 x ^ { 2 } + 47 x ^ { 2 } - 7 = 0$$

x uchun yechish

$$x=\frac{\sqrt{14}}{10}\approx 0,374165739$$

$$x=-\frac{\sqrt{14}}{10}\approx -0,374165739$$

Kvadrat ildizini topish bo'yicha qadamlar

50x^{2} ni olish uchun 3x^{2} va 47x^{2} ni birlashtirish.

$$50x^{2}-7=0$$

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

$$50x^{2}=7$$

Ikki tarafini 50 ga bo‘ling.

$$x^{2}=\frac{7}{50}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=\frac{\sqrt{14}}{10} x=-\frac{\sqrt{14}}{10}$$

Kvadrat tenglamalaridan foydalanish qoidalari

50x^{2} ni olish uchun 3x^{2} va 47x^{2} ni birlashtirish.

$$50x^{2}-7=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 50 ni a, 0 ni b va -7 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 50\left(-7\right)}}{2\times 50}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 50\left(-7\right)}}{2\times 50}$$

-4 ni 50 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-200\left(-7\right)}}{2\times 50}$$

-200 ni -7 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{1400}}{2\times 50}$$

1400 ning kvadrat ildizini chiqarish.

$$x=\frac{0±10\sqrt{14}}{2\times 50}$$

2 ni 50 marotabaga ko'paytirish.

$$x=\frac{0±10\sqrt{14}}{100}$$

x=\frac{0±10\sqrt{14}}{100} tenglamasini yeching, bunda ± musbat.

$$x=\frac{\sqrt{14}}{10}$$

x=\frac{0±10\sqrt{14}}{100} tenglamasini yeching, bunda ± manfiy.

$$x=-\frac{\sqrt{14}}{10}$$

Tenglama yechildi.

$$x=\frac{\sqrt{14}}{10} x=-\frac{\sqrt{14}}{10}$$