x^2=729/4 eching

$$x ^ { 2 } = \frac { 729 } { 4 }$$

x uchun yechish

$$x = \frac{27}{2} = 13\frac{1}{2} = 13,5$$

$$x = -\frac{27}{2} = -13\frac{1}{2} = -13,5$$

Kvadratlar farqidan foydalangan qadamlar

Ikkala tarafdan \frac{729}{4} ni ayirish.

$$x^{2}-\frac{729}{4}=0$$

Ikkala tarafini 4 ga ko‘paytiring.

$$4x^{2}-729=0$$

Hisoblang: 4x^{2}-729. 4x^{2}-729 ni \left(2x\right)^{2}-27^{2} sifatida qaytadan yozish. Kvadratlarning farqini ushbu formula bilan hisoblash mumkin: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(2x-27\right)\left(2x+27\right)=0$$

Tenglamani yechish uchun 2x-27=0 va 2x+27=0 ni yeching.

$$x=\frac{27}{2} x=-\frac{27}{2}$$

Kvadrat ildizini topish bo'yicha qadamlar

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=\frac{27}{2} x=-\frac{27}{2}$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan \frac{729}{4} ni ayirish.

$$x^{2}-\frac{729}{4}=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 0 ni b va -\frac{729}{4} ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{729}{4}\right)}}{2}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\left(-\frac{729}{4}\right)}}{2}$$

-4 ni -\frac{729}{4} marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{729}}{2}$$

729 ning kvadrat ildizini chiqarish.

$$x=\frac{0±27}{2}$$

x=\frac{0±27}{2} tenglamasini yeching, bunda ± musbat. 27 ni 2 ga bo'lish.

$$x=\frac{27}{2}$$

x=\frac{0±27}{2} tenglamasini yeching, bunda ± manfiy. -27 ni 2 ga bo'lish.

$$x=-\frac{27}{2}$$

Tenglama yechildi.

$$x=\frac{27}{2} x=-\frac{27}{2}$$