2x^2=102/-2+5^2 eching

$$2 x ^ { 2 } = 10 \frac { 2 } { - 2 } + 5 ^ { 2 }$$

x uchun yechish

$$x=\sqrt{17}\approx 4,123105626$$

$$x=-\sqrt{17}\approx -4,123105626$$

Kvadrat ildizini topish bo'yicha qadamlar

Tenglamaning ikkala tarafini -2 ga ko'paytirish.

$$-4x^{2}=10\left(-2\right)+2-2\times 5^{2}$$

-20 hosil qilish uchun 10 va -2 ni ko'paytirish.

$$-4x^{2}=-20+2-2\times 5^{2}$$

-18 olish uchun -20 va 2'ni qo'shing.

$$-4x^{2}=-18-2\times 5^{2}$$

2 daraja ko‘rsatkichini 5 ga hisoblang va 25 ni qiymatni oling.

$$-4x^{2}=-18-2\times 25$$

-50 hosil qilish uchun -2 va 25 ni ko'paytirish.

$$-4x^{2}=-18-50$$

-68 olish uchun -18 dan 50 ni ayirish.

$$-4x^{2}=-68$$

Ikki tarafini -4 ga bo‘ling.

$$x^{2}=\frac{-68}{-4}$$

17 ni olish uchun -68 ni -4 ga bo‘ling.

$$x^{2}=17$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=\sqrt{17} x=-\sqrt{17}$$

Kvadrat tenglamalaridan foydalanish qoidalari

Tenglamaning ikkala tarafini -2 ga ko'paytirish.

$$-4x^{2}=10\left(-2\right)+2-2\times 5^{2}$$

-20 hosil qilish uchun 10 va -2 ni ko'paytirish.

$$-4x^{2}=-20+2-2\times 5^{2}$$

-18 olish uchun -20 va 2'ni qo'shing.

$$-4x^{2}=-18-2\times 5^{2}$$

2 daraja ko‘rsatkichini 5 ga hisoblang va 25 ni qiymatni oling.

$$-4x^{2}=-18-2\times 25$$

-50 hosil qilish uchun -2 va 25 ni ko'paytirish.

$$-4x^{2}=-18-50$$

-68 olish uchun -18 dan 50 ni ayirish.

$$-4x^{2}=-68$$

68 ni ikki tarafga qo’shing.

$$-4x^{2}+68=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -4 ni a, 0 ni b va 68 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\left(-4\right)\times 68}}{2\left(-4\right)}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\left(-4\right)\times 68}}{2\left(-4\right)}$$

-4 ni -4 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{16\times 68}}{2\left(-4\right)}$$

16 ni 68 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{1088}}{2\left(-4\right)}$$

1088 ning kvadrat ildizini chiqarish.

$$x=\frac{0±8\sqrt{17}}{2\left(-4\right)}$$

2 ni -4 marotabaga ko'paytirish.

$$x=\frac{0±8\sqrt{17}}{-8}$$

x=\frac{0±8\sqrt{17}}{-8} tenglamasini yeching, bunda ± musbat.

$$x=-\sqrt{17}$$

x=\frac{0±8\sqrt{17}}{-8} tenglamasini yeching, bunda ± manfiy.

$$x=\sqrt{17}$$

Tenglama yechildi.

$$x=-\sqrt{17} x=\sqrt{17}$$