2x^2+7=207 eching

$$2 x ^ { 2 } + 7 = 207$$

x uchun yechish

$$x=10$$

$$x=-10$$

Kvadratlar farqidan foydalangan qadamlar

Ikkala tarafdan 207 ni ayirish.

$$2x^{2}+7-207=0$$

-200 olish uchun 7 dan 207 ni ayirish.

$$2x^{2}-200=0$$

Ikki tarafini 2 ga bo‘ling.

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

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

Ikkala tarafdan 7 ni ayirish.

$$2x^{2}=207-7$$

200 olish uchun 207 dan 7 ni ayirish.

$$2x^{2}=200$$

Ikki tarafini 2 ga bo‘ling.

$$x^{2}=\frac{200}{2}$$

100 ni olish uchun 200 ni 2 ga bo‘ling.

$$x^{2}=100$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=10 x=-10$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 207 ni ayirish.

$$2x^{2}+7-207=0$$

-200 olish uchun 7 dan 207 ni ayirish.

$$2x^{2}-200=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 2 ni a, 0 ni b va -200 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-200\right)}}{2\times 2}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 2\left(-200\right)}}{2\times 2}$$

-4 ni 2 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-8\left(-200\right)}}{2\times 2}$$

-8 ni -200 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{1600}}{2\times 2}$$

1600 ning kvadrat ildizini chiqarish.

$$x=\frac{0±40}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$x=\frac{0±40}{4}$$

x=\frac{0±40}{4} tenglamasini yeching, bunda ± musbat. 40 ni 4 ga bo'lish.

$$x=10$$

x=\frac{0±40}{4} tenglamasini yeching, bunda ± manfiy. -40 ni 4 ga bo'lish.

$$x=-10$$

Tenglama yechildi.

$$x=10 x=-10$$