y^2=18y eching

$$y ^ { 2 } = 18 y$$

y uchun yechish

$$y=18$$

$$y=0$$

Faktorlash qadamlari

Ikkala tarafdan 18y ni ayirish.

$$y^{2}-18y=0$$

y omili.

$$y\left(y-18\right)=0$$

Tenglamani yechish uchun y=0 va y-18=0 ni yeching.

$$y=0 y=18$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 18y ni ayirish.

$$y^{2}-18y=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -18 ni b va 0 ni c bilan almashtiring.

$$y=\frac{-\left(-18\right)±\sqrt{\left(-18\right)^{2}}}{2}$$

\left(-18\right)^{2} ning kvadrat ildizini chiqarish.

$$y=\frac{-\left(-18\right)±18}{2}$$

-18 ning teskarisi 18 ga teng.

$$y=\frac{18±18}{2}$$

y=\frac{18±18}{2} tenglamasini yeching, bunda ± musbat. 18 ni 18 ga qo'shish.

$$y=\frac{36}{2}$$

36 ni 2 ga bo'lish.

$$y=18$$

y=\frac{18±18}{2} tenglamasini yeching, bunda ± manfiy. 18 dan 18 ni ayirish.

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

0 ni 2 ga bo'lish.

$$y=0$$

Tenglama yechildi.

$$y=18 y=0$$

Kvadratni yakunlash bo'yicha qadamlar

Ikkala tarafdan 18y ni ayirish.

$$y^{2}-18y=0$$

-18 ni bo‘lish, x shartining koeffitsienti, 2 ga -9 olish uchun. Keyin, -9 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$y^{2}-18y+\left(-9\right)^{2}=\left(-9\right)^{2}$$

-9 kvadratini chiqarish.

$$y^{2}-18y+81=81$$

y^{2}-18y+81 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(y-9\right)^{2}=81$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(y-9\right)^{2}}=\sqrt{81}$$

Qisqartirish.

$$y-9=9 y-9=-9$$

9 ni tenglamaning ikkala tarafiga qo'shish.

$$y=18 y=0$$