(1/2)200t^2=10000 eching

$$( 1 / 2 ) 200 t ^ { 2 } = 10000$$

t uchun yechish

$$t=10$$

$$t=-10$$

Kvadratlar farqidan foydalangan qadamlar

100 hosil qilish uchun \frac{1}{2} va 200 ni ko'paytirish.

$$100t^{2}=10000$$

Ikkala tarafdan 10000 ni ayirish.

$$100t^{2}-10000=0$$

Ikki tarafini 100 ga bo‘ling.

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

Hisoblang: t^{2}-100. t^{2}-100 ni t^{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).

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

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

$$t=10 t=-10$$

Kvadrat ildizini topish bo'yicha qadamlar

100 hosil qilish uchun \frac{1}{2} va 200 ni ko'paytirish.

$$100t^{2}=10000$$

Ikki tarafini 100 ga bo‘ling.

$$t^{2}=\frac{10000}{100}$$

100 ni olish uchun 10000 ni 100 ga bo‘ling.

$$t^{2}=100$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$t=10 t=-10$$

Kvadrat tenglamalaridan foydalanish qoidalari

100 hosil qilish uchun \frac{1}{2} va 200 ni ko'paytirish.

$$100t^{2}=10000$$

Ikkala tarafdan 10000 ni ayirish.

$$100t^{2}-10000=0$$

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 -10000 ni c bilan almashtiring.

$$t=\frac{0±\sqrt{0^{2}-4\times 100\left(-10000\right)}}{2\times 100}$$

0 kvadratini chiqarish.

$$t=\frac{0±\sqrt{-4\times 100\left(-10000\right)}}{2\times 100}$$

-4 ni 100 marotabaga ko'paytirish.

$$t=\frac{0±\sqrt{-400\left(-10000\right)}}{2\times 100}$$

-400 ni -10000 marotabaga ko'paytirish.

$$t=\frac{0±\sqrt{4000000}}{2\times 100}$$

4000000 ning kvadrat ildizini chiqarish.

$$t=\frac{0±2000}{2\times 100}$$

2 ni 100 marotabaga ko'paytirish.

$$t=\frac{0±2000}{200}$$

t=\frac{0±2000}{200} tenglamasini yeching, bunda ± musbat. 2000 ni 200 ga bo'lish.

$$t=10$$

t=\frac{0±2000}{200} tenglamasini yeching, bunda ± manfiy. -2000 ni 200 ga bo'lish.

$$t=-10$$

Tenglama yechildi.

$$t=10 t=-10$$