Whakaoti i te 3y^2=-21y

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

Whakaoti mō y

$$y=-7$$

$$y=0$$

Ngā Upane Whakamahi Tauwehe

Me tāpiri te 21y ki ngā taha e rua.

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

Tauwehea te y.

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

Hei kimi otinga whārite, me whakaoti te y=0 me te 3y+21=0.

$$y=0 y=-7$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Me tāpiri te 21y ki ngā taha e rua.

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

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 3 mō a, 21 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

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

Tuhia te pūtakerua o te 21^{2}.

$$y=\frac{-21±21}{2\times 3}$$

Whakareatia 2 ki te 3.

$$y=\frac{-21±21}{6}$$

Nā, me whakaoti te whārite y=\frac{-21±21}{6} ina he tāpiri te ±. Tāpiri -21 ki te 21.

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

Whakawehe 0 ki te 6.

$$y=0$$

Nā, me whakaoti te whārite y=\frac{-21±21}{6} ina he tango te ±. Tango 21 mai i -21.

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

Whakawehe -42 ki te 6.

$$y=-7$$

Kua oti te whārite te whakatau.

$$y=0 y=-7$$

Ngā Upane mō te Whakaoti i te Pūrua

Me tāpiri te 21y ki ngā taha e rua.

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

Whakawehea ngā taha e rua ki te 3.

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

Mā te whakawehe ki te 3 ka wetekia te whakareanga ki te 3.

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

Whakawehe 21 ki te 3.

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

Whakawehe 0 ki te 3.

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

Whakawehea te 7, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{7}{2}. Nā, tāpiria te pūrua o te \frac{7}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

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

Pūruatia \frac{7}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

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

Tauwehea y^{2}+7y+\frac{49}{4}. Ko te tikanga pūnoa, ina ko x^{2}+bx+c he pūrua tika pūrua tika pū, ka taea taua mea te tauwehea i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.

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

Tuhia te pūtakerua o ngā taha e rua o te whārite.

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

Whakarūnātia.

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

Me tango \frac{7}{2} mai i ngā taha e rua o te whārite.

$$y=0 y=-7$$