5x^2+9=54 eching

$$5 x ^ { 2 } + 9 = 54$$

x uchun yechish

$$x=3$$

$$x=-3$$

Kvadratlar farqidan foydalangan qadamlar

Ikkala tarafdan 54 ni ayirish.

$$5x^{2}+9-54=0$$

-45 olish uchun 9 dan 54 ni ayirish.

$$5x^{2}-45=0$$

Ikki tarafini 5 ga bo‘ling.

$$x^{2}-9=0$$

Hisoblang: x^{2}-9. x^{2}-9 ni x^{2}-3^{2} sifatida qaytadan yozish. Kvadratlarning farqini ushbu formula bilan hisoblash mumkin: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-3\right)\left(x+3\right)=0$$

Tenglamani yechish uchun x-3=0 va x+3=0 ni yeching.

$$x=3 x=-3$$

Kvadrat ildizini topish bo'yicha qadamlar

Ikkala tarafdan 9 ni ayirish.

$$5x^{2}=54-9$$

45 olish uchun 54 dan 9 ni ayirish.

$$5x^{2}=45$$

Ikki tarafini 5 ga bo‘ling.

$$x^{2}=\frac{45}{5}$$

9 ni olish uchun 45 ni 5 ga bo‘ling.

$$x^{2}=9$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=3 x=-3$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 54 ni ayirish.

$$5x^{2}+9-54=0$$

-45 olish uchun 9 dan 54 ni ayirish.

$$5x^{2}-45=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 5 ni a, 0 ni b va -45 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 5\left(-45\right)}}{2\times 5}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 5\left(-45\right)}}{2\times 5}$$

-4 ni 5 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-20\left(-45\right)}}{2\times 5}$$

-20 ni -45 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{900}}{2\times 5}$$

900 ning kvadrat ildizini chiqarish.

$$x=\frac{0±30}{2\times 5}$$

2 ni 5 marotabaga ko'paytirish.

$$x=\frac{0±30}{10}$$

x=\frac{0±30}{10} tenglamasini yeching, bunda ± musbat. 30 ni 10 ga bo'lish.

$$x=3$$

x=\frac{0±30}{10} tenglamasini yeching, bunda ± manfiy. -30 ni 10 ga bo'lish.

$$x=-3$$

Tenglama yechildi.

$$x=3 x=-3$$