x^2=25x eching

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

x uchun yechish

$$x=25$$

$$x=0$$

Faktorlash qadamlari

Ikkala tarafdan 25x ni ayirish.

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

x omili.

$$x\left(x-25\right)=0$$

Tenglamani yechish uchun x=0 va x-25=0 ni yeching.

$$x=0 x=25$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 25x ni ayirish.

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

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -25 ni b va 0 ni c bilan almashtiring.

$$x=\frac{-\left(-25\right)±\sqrt{\left(-25\right)^{2}}}{2}$$

\left(-25\right)^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-25\right)±25}{2}$$

-25 ning teskarisi 25 ga teng.

$$x=\frac{25±25}{2}$$

x=\frac{25±25}{2} tenglamasini yeching, bunda ± musbat. 25 ni 25 ga qo'shish.

$$x=\frac{50}{2}$$

50 ni 2 ga bo'lish.

$$x=25$$

x=\frac{25±25}{2} tenglamasini yeching, bunda ± manfiy. 25 dan 25 ni ayirish.

$$x=\frac{0}{2}$$

0 ni 2 ga bo'lish.

$$x=0$$

Tenglama yechildi.

$$x=25 x=0$$

Kvadratni yakunlash bo'yicha qadamlar

Ikkala tarafdan 25x ni ayirish.

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

-25 ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{25}{2} olish uchun. Keyin, -\frac{25}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-25x+\left(-\frac{25}{2}\right)^{2}=\left(-\frac{25}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{25}{2} kvadratini chiqarish.

$$x^{2}-25x+\frac{625}{4}=\frac{625}{4}$$

x^{2}-25x+\frac{625}{4} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{25}{2}\right)^{2}=\frac{625}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{25}{2}\right)^{2}}=\sqrt{\frac{625}{4}}$$

Qisqartirish.

$$x-\frac{25}{2}=\frac{25}{2} x-\frac{25}{2}=-\frac{25}{2}$$

\frac{25}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$x=25 x=0$$