15625x^2=100 eching

$$15625 x ^ { 2 } = 100$$

x uchun yechish

$$x=\frac{2}{25}=0,08$$

$$x=-\frac{2}{25}=-0,08$$

Kvadratlar farqidan foydalangan qadamlar

Ikki tarafini 15625 ga bo‘ling.

$$x^{2}=\frac{100}{15625}$$

\frac{100}{15625} ulushini 25 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}=\frac{4}{625}$$

Ikkala tarafdan \frac{4}{625} ni ayirish.

$$x^{2}-\frac{4}{625}=0$$

Ikkala tarafini 625 ga ko‘paytiring.

$$625x^{2}-4=0$$

Hisoblang: 625x^{2}-4. 625x^{2}-4 ni \left(25x\right)^{2}-2^{2} sifatida qaytadan yozish. Kvadratlarning farqini ushbu formula bilan hisoblash mumkin: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(25x-2\right)\left(25x+2\right)=0$$

Tenglamani yechish uchun 25x-2=0 va 25x+2=0 ni yeching.

$$x=\frac{2}{25} x=-\frac{2}{25}$$

Kvadrat ildizini topish bo'yicha qadamlar

Ikki tarafini 15625 ga bo‘ling.

$$x^{2}=\frac{100}{15625}$$

\frac{100}{15625} ulushini 25 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}=\frac{4}{625}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=\frac{2}{25} x=-\frac{2}{25}$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikki tarafini 15625 ga bo‘ling.

$$x^{2}=\frac{100}{15625}$$

\frac{100}{15625} ulushini 25 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}=\frac{4}{625}$$

Ikkala tarafdan \frac{4}{625} ni ayirish.

$$x^{2}-\frac{4}{625}=0$$

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 -\frac{4}{625} ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{4}{625}\right)}}{2}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\left(-\frac{4}{625}\right)}}{2}$$

-4 ni -\frac{4}{625} marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{\frac{16}{625}}}{2}$$

\frac{16}{625} ning kvadrat ildizini chiqarish.

$$x=\frac{0±\frac{4}{25}}{2}$$

x=\frac{0±\frac{4}{25}}{2} tenglamasini yeching, bunda ± musbat.

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

x=\frac{0±\frac{4}{25}}{2} tenglamasini yeching, bunda ± manfiy.

$$x=-\frac{2}{25}$$

Tenglama yechildi.

$$x=\frac{2}{25} x=-\frac{2}{25}$$