180/360(x^2)*pi=50pi eching

$$\frac{ 180 }{ 360 } ( { x }^{ 2 } ) \times \pi =50 \pi$$

x uchun yechish

$$x=10$$

$$x=-10$$

Kvadratlar farqidan foydalangan qadamlar

\pi ni ikki tarafidan bekor qilish.

$$\frac{180}{360}x^{2}=50$$

\frac{180}{360} ulushini 180 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{1}{2}x^{2}=50$$

Ikkala tarafdan 50 ni ayirish.

$$\frac{1}{2}x^{2}-50=0$$

Ikkala tarafini 2 ga ko‘paytiring.

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

Hisoblang: x^{2}-100. x^{2}-100 ni x^{2}-10^{2} sifatida qaytadan yozish. Kvadratlarning farqini ushbu formula bilan hisoblash mumkin: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-10\right)\left(x+10\right)=0$$

Tenglamani yechish uchun x-10=0 va x+10=0 ni yeching.

$$x=10 x=-10$$

Kvadrat ildizini topish bo'yicha qadamlar

\pi ni ikki tarafidan bekor qilish.

$$\frac{180}{360}x^{2}=50$$

\frac{180}{360} ulushini 180 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{1}{2}x^{2}=50$$

Ikki tarafini 2 va teskari kasri \frac{1}{2} ga ko‘paytiring.

$$x^{2}=50\times 2$$

100 hosil qilish uchun 50 va 2 ni ko'paytirish.

$$x^{2}=100$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=10 x=-10$$

Kvadrat tenglamalaridan foydalanish qoidalari

\pi ni ikki tarafidan bekor qilish.

$$\frac{180}{360}x^{2}=50$$

\frac{180}{360} ulushini 180 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{1}{2}x^{2}=50$$

Ikkala tarafdan 50 ni ayirish.

$$\frac{1}{2}x^{2}-50=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} \frac{1}{2} ni a, 0 ni b va -50 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{1}{2}\left(-50\right)}}{2\times \frac{1}{2}}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times \frac{1}{2}\left(-50\right)}}{2\times \frac{1}{2}}$$

-4 ni \frac{1}{2} marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-2\left(-50\right)}}{2\times \frac{1}{2}}$$

-2 ni -50 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{100}}{2\times \frac{1}{2}}$$

100 ning kvadrat ildizini chiqarish.

$$x=\frac{0±10}{2\times \frac{1}{2}}$$

2 ni \frac{1}{2} marotabaga ko'paytirish.

$$x=\frac{0±10}{1}$$

x=\frac{0±10}{1} tenglamasini yeching, bunda ± musbat.

$$x=10$$

x=\frac{0±10}{1} tenglamasini yeching, bunda ± manfiy.

$$x=-10$$

Tenglama yechildi.

$$x=10 x=-10$$