5x^2-4=1900 eching

$$5 x ^ { 2 } - 4 = 1900$$

x uchun yechish

$$x = \frac{4 \sqrt{595}}{5} \approx 19,514097468$$

$$x = -\frac{4 \sqrt{595}}{5} \approx -19,514097468$$

Kvadrat ildizini topish bo'yicha qadamlar

4 ni ikki tarafga qo’shing.

$$5x^{2}=1900+4$$

1904 olish uchun 1900 va 4'ni qo'shing.

$$5x^{2}=1904$$

Ikki tarafini 5 ga bo‘ling.

$$x^{2}=\frac{1904}{5}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=\frac{4\sqrt{595}}{5} x=-\frac{4\sqrt{595}}{5}$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 1900 ni ayirish.

$$5x^{2}-4-1900=0$$

-1904 olish uchun -4 dan 1900 ni ayirish.

$$5x^{2}-1904=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 5 ni a, 0 ni b va -1904 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 5\left(-1904\right)}}{2\times 5}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 5\left(-1904\right)}}{2\times 5}$$

-4 ni 5 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-20\left(-1904\right)}}{2\times 5}$$

-20 ni -1904 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{38080}}{2\times 5}$$

38080 ning kvadrat ildizini chiqarish.

$$x=\frac{0±8\sqrt{595}}{2\times 5}$$

2 ni 5 marotabaga ko'paytirish.

$$x=\frac{0±8\sqrt{595}}{10}$$

x=\frac{0±8\sqrt{595}}{10} tenglamasini yeching, bunda ± musbat.

$$x=\frac{4\sqrt{595}}{5}$$

x=\frac{0±8\sqrt{595}}{10} tenglamasini yeching, bunda ± manfiy.

$$x=-\frac{4\sqrt{595}}{5}$$

Tenglama yechildi.

$$x=\frac{4\sqrt{595}}{5} x=-\frac{4\sqrt{595}}{5}$$