100x^2-225=+11 eching

$$100 x ^ { 2 } - 225 = + 11$$

x uchun yechish

$$x = \frac{\sqrt{59}}{5} \approx 1,53622915$$

$$x = -\frac{\sqrt{59}}{5} \approx -1,53622915$$

Kvadrat ildizini topish bo'yicha qadamlar

225 ni ikki tarafga qo’shing.

$$100x^{2}=11+225$$

236 olish uchun 11 va 225'ni qo'shing.

$$100x^{2}=236$$

Ikki tarafini 100 ga bo‘ling.

$$x^{2}=\frac{236}{100}$$

\frac{236}{100} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}=\frac{59}{25}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=\frac{\sqrt{59}}{5} x=-\frac{\sqrt{59}}{5}$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 11 ni ayirish.

$$100x^{2}-225-11=0$$

-236 olish uchun -225 dan 11 ni ayirish.

$$100x^{2}-236=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 100 ni a, 0 ni b va -236 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 100\left(-236\right)}}{2\times 100}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 100\left(-236\right)}}{2\times 100}$$

-4 ni 100 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-400\left(-236\right)}}{2\times 100}$$

-400 ni -236 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{94400}}{2\times 100}$$

94400 ning kvadrat ildizini chiqarish.

$$x=\frac{0±40\sqrt{59}}{2\times 100}$$

2 ni 100 marotabaga ko'paytirish.

$$x=\frac{0±40\sqrt{59}}{200}$$

x=\frac{0±40\sqrt{59}}{200} tenglamasini yeching, bunda ± musbat.

$$x=\frac{\sqrt{59}}{5}$$

x=\frac{0±40\sqrt{59}}{200} tenglamasini yeching, bunda ± manfiy.

$$x=-\frac{\sqrt{59}}{5}$$

Tenglama yechildi.

$$x=\frac{\sqrt{59}}{5} x=-\frac{\sqrt{59}}{5}$$