2x^2+17=179 eching

$$2 { x }^{ 2 } +17=179$$

x uchun yechish

$$x=9$$

$$x=-9$$

Kvadratlar farqidan foydalangan qadamlar

Ikkala tarafdan 179 ni ayirish.

$$2x^{2}+17-179=0$$

-162 olish uchun 17 dan 179 ni ayirish.

$$2x^{2}-162=0$$

Ikki tarafini 2 ga bo‘ling.

$$x^{2}-81=0$$

Hisoblang: x^{2}-81. x^{2}-81 ni x^{2}-9^{2} sifatida qaytadan yozish. Kvadratlarning farqini ushbu formula bilan hisoblash mumkin: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-9\right)\left(x+9\right)=0$$

Tenglamani yechish uchun x-9=0 va x+9=0 ni yeching.

$$x=9 x=-9$$

Kvadrat ildizini topish bo'yicha qadamlar

Ikkala tarafdan 17 ni ayirish.

$$2x^{2}=179-17$$

162 olish uchun 179 dan 17 ni ayirish.

$$2x^{2}=162$$

Ikki tarafini 2 ga bo‘ling.

$$x^{2}=\frac{162}{2}$$

81 ni olish uchun 162 ni 2 ga bo‘ling.

$$x^{2}=81$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=9 x=-9$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 179 ni ayirish.

$$2x^{2}+17-179=0$$

-162 olish uchun 17 dan 179 ni ayirish.

$$2x^{2}-162=0$$

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 -162 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-162\right)}}{2\times 2}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 2\left(-162\right)}}{2\times 2}$$

-4 ni 2 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-8\left(-162\right)}}{2\times 2}$$

-8 ni -162 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{1296}}{2\times 2}$$

1296 ning kvadrat ildizini chiqarish.

$$x=\frac{0±36}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$x=\frac{0±36}{4}$$

x=\frac{0±36}{4} tenglamasini yeching, bunda ± musbat. 36 ni 4 ga bo'lish.

$$x=9$$

x=\frac{0±36}{4} tenglamasini yeching, bunda ± manfiy. -36 ni 4 ga bo'lish.

$$x=-9$$

Tenglama yechildi.

$$x=9 x=-9$$