4x^2-30=34 eching

$$4 x ^ { 2 } - 30 = 34$$

x uchun yechish

$$x=4$$

$$x=-4$$

Kvadratlar farqidan foydalangan qadamlar

Ikkala tarafdan 34 ni ayirish.

$$4x^{2}-30-34=0$$

-64 olish uchun -30 dan 34 ni ayirish.

$$4x^{2}-64=0$$

Ikki tarafini 4 ga bo‘ling.

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

Hisoblang: x^{2}-16. x^{2}-16 ni x^{2}-4^{2} sifatida qaytadan yozish. Kvadratlarning farqini ushbu formula bilan hisoblash mumkin: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-4\right)\left(x+4\right)=0$$

Tenglamani yechish uchun x-4=0 va x+4=0 ni yeching.

$$x=4 x=-4$$

Kvadrat ildizini topish bo'yicha qadamlar

30 ni ikki tarafga qo’shing.

$$4x^{2}=34+30$$

64 olish uchun 34 va 30'ni qo'shing.

$$4x^{2}=64$$

Ikki tarafini 4 ga bo‘ling.

$$x^{2}=\frac{64}{4}$$

16 ni olish uchun 64 ni 4 ga bo‘ling.

$$x^{2}=16$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=4 x=-4$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 34 ni ayirish.

$$4x^{2}-30-34=0$$

-64 olish uchun -30 dan 34 ni ayirish.

$$4x^{2}-64=0$$

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 -64 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 4\left(-64\right)}}{2\times 4}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 4\left(-64\right)}}{2\times 4}$$

-4 ni 4 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-16\left(-64\right)}}{2\times 4}$$

-16 ni -64 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{1024}}{2\times 4}$$

1024 ning kvadrat ildizini chiqarish.

$$x=\frac{0±32}{2\times 4}$$

2 ni 4 marotabaga ko'paytirish.

$$x=\frac{0±32}{8}$$

x=\frac{0±32}{8} tenglamasini yeching, bunda ± musbat. 32 ni 8 ga bo'lish.

$$x=4$$

x=\frac{0±32}{8} tenglamasini yeching, bunda ± manfiy. -32 ni 8 ga bo'lish.

$$x=-4$$

Tenglama yechildi.

$$x=4 x=-4$$