x^2-14=5x+67-5x eching

$$x ^ { 2 } - 14 = 5 x + 67 - 5 x$$

x uchun yechish

$$x=9$$

$$x=-9$$

Kvadratlar farqidan foydalangan qadamlar

0 ni olish uchun 5x va -5x ni birlashtirish.

$$x^{2}-14=67$$

Ikkala tarafdan 67 ni ayirish.

$$x^{2}-14-67=0$$

-81 olish uchun -14 dan 67 ni ayirish.

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

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

0 ni olish uchun 5x va -5x ni birlashtirish.

$$x^{2}-14=67$$

14 ni ikki tarafga qo’shing.

$$x^{2}=67+14$$

81 olish uchun 67 va 14'ni qo'shing.

$$x^{2}=81$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=9 x=-9$$

Kvadrat tenglamalaridan foydalanish qoidalari

0 ni olish uchun 5x va -5x ni birlashtirish.

$$x^{2}-14=67$$

Ikkala tarafdan 67 ni ayirish.

$$x^{2}-14-67=0$$

-81 olish uchun -14 dan 67 ni ayirish.

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

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 -81 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\left(-81\right)}}{2}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\left(-81\right)}}{2}$$

-4 ni -81 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{324}}{2}$$

324 ning kvadrat ildizini chiqarish.

$$x=\frac{0±18}{2}$$

x=\frac{0±18}{2} tenglamasini yeching, bunda ± musbat. 18 ni 2 ga bo'lish.

$$x=9$$

x=\frac{0±18}{2} tenglamasini yeching, bunda ± manfiy. -18 ni 2 ga bo'lish.

$$x=-9$$

Tenglama yechildi.

$$x=9 x=-9$$