3y^2=-21y eching

$$3 y ^ { 2 } = - 21 y$$

y uchun yechish

$$y=-7$$

$$y=0$$

Faktorlash qadamlari

21y ni ikki tarafga qo’shing.

$$3y^{2}+21y=0$$

y omili.

$$y\left(3y+21\right)=0$$

Tenglamani yechish uchun y=0 va 3y+21=0 ni yeching.

$$y=0 y=-7$$

Kvadrat tenglamalaridan foydalanish qoidalari

21y ni ikki tarafga qo’shing.

$$3y^{2}+21y=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 3 ni a, 21 ni b va 0 ni c bilan almashtiring.

$$y=\frac{-21±\sqrt{21^{2}}}{2\times 3}$$

21^{2} ning kvadrat ildizini chiqarish.

$$y=\frac{-21±21}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$y=\frac{-21±21}{6}$$

y=\frac{-21±21}{6} tenglamasini yeching, bunda ± musbat. -21 ni 21 ga qo'shish.

$$y=\frac{0}{6}$$

0 ni 6 ga bo'lish.

$$y=0$$

y=\frac{-21±21}{6} tenglamasini yeching, bunda ± manfiy. -21 dan 21 ni ayirish.

$$y=-\frac{42}{6}$$

-42 ni 6 ga bo'lish.

$$y=-7$$

Tenglama yechildi.

$$y=0 y=-7$$

Kvadratni yakunlash bo'yicha qadamlar

21y ni ikki tarafga qo’shing.

$$3y^{2}+21y=0$$

Ikki tarafini 3 ga bo‘ling.

$$\frac{3y^{2}+21y}{3}=\frac{0}{3}$$

3 ga bo'lish 3 ga ko'paytirishni bekor qiladi.

$$y^{2}+\frac{21}{3}y=\frac{0}{3}$$

21 ni 3 ga bo'lish.

$$y^{2}+7y=\frac{0}{3}$$

0 ni 3 ga bo'lish.

$$y^{2}+7y=0$$

7 ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{7}{2} olish uchun. Keyin, \frac{7}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$y^{2}+7y+\left(\frac{7}{2}\right)^{2}=\left(\frac{7}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{7}{2} kvadratini chiqarish.

$$y^{2}+7y+\frac{49}{4}=\frac{49}{4}$$

y^{2}+7y+\frac{49}{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.

$$\left(y+\frac{7}{2}\right)^{2}=\frac{49}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(y+\frac{7}{2}\right)^{2}}=\sqrt{\frac{49}{4}}$$

Qisqartirish.

$$y+\frac{7}{2}=\frac{7}{2} y+\frac{7}{2}=-\frac{7}{2}$$

Tenglamaning ikkala tarafidan \frac{7}{2} ni ayirish.

$$y=0 y=-7$$