(x+5)(x-5)=24 eching

$$( x + 5 ) ( x - 5 ) = 24$$

x uchun yechish

$$x=-7$$

$$x=7$$

Kvadrat ildizini topish bo'yicha qadamlar

Hisoblang: \left(x+5\right)\left(x-5\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. 5 kvadratini chiqarish.

$$x^{2}-25=24$$

25 ni ikki tarafga qo’shing.

$$x^{2}=24+25$$

49 olish uchun 24 va 25'ni qo'shing.

$$x^{2}=49$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=7 x=-7$$

Kvadrat tenglamalaridan foydalanish qoidalari

Hisoblang: \left(x+5\right)\left(x-5\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. 5 kvadratini chiqarish.

$$x^{2}-25=24$$

Ikkala tarafdan 24 ni ayirish.

$$x^{2}-25-24=0$$

-49 olish uchun -25 dan 24 ni ayirish.

$$x^{2}-49=0$$

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 -49 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\left(-49\right)}}{2}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\left(-49\right)}}{2}$$

-4 ni -49 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{196}}{2}$$

196 ning kvadrat ildizini chiqarish.

$$x=\frac{0±14}{2}$$

x=\frac{0±14}{2} tenglamasini yeching, bunda ± musbat. 14 ni 2 ga bo'lish.

$$x=7$$

x=\frac{0±14}{2} tenglamasini yeching, bunda ± manfiy. -14 ni 2 ga bo'lish.

$$x=-7$$

Tenglama yechildi.

$$x=7 x=-7$$