16x^2+49=100 eching

$$16 x ^ { 2 } + 49 = 100$$

x uchun yechish

$$x = \frac{\sqrt{51}}{4} \approx 1,785357107$$

$$x = -\frac{\sqrt{51}}{4} \approx -1,785357107$$

Kvadrat ildizini topish bo'yicha qadamlar

Ikkala tarafdan 49 ni ayirish.

$$16x^{2}=100-49$$

51 olish uchun 100 dan 49 ni ayirish.

$$16x^{2}=51$$

Ikki tarafini 16 ga bo‘ling.

$$x^{2}=\frac{51}{16}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=\frac{\sqrt{51}}{4} x=-\frac{\sqrt{51}}{4}$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 100 ni ayirish.

$$16x^{2}+49-100=0$$

-51 olish uchun 49 dan 100 ni ayirish.

$$16x^{2}-51=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 16 ni a, 0 ni b va -51 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 16\left(-51\right)}}{2\times 16}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 16\left(-51\right)}}{2\times 16}$$

-4 ni 16 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-64\left(-51\right)}}{2\times 16}$$

-64 ni -51 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{3264}}{2\times 16}$$

3264 ning kvadrat ildizini chiqarish.

$$x=\frac{0±8\sqrt{51}}{2\times 16}$$

2 ni 16 marotabaga ko'paytirish.

$$x=\frac{0±8\sqrt{51}}{32}$$

x=\frac{0±8\sqrt{51}}{32} tenglamasini yeching, bunda ± musbat.

$$x=\frac{\sqrt{51}}{4}$$

x=\frac{0±8\sqrt{51}}{32} tenglamasini yeching, bunda ± manfiy.

$$x=-\frac{\sqrt{51}}{4}$$

Tenglama yechildi.

$$x=\frac{\sqrt{51}}{4} x=-\frac{\sqrt{51}}{4}$$