Whakaoti i te 9n^2+21n=0

$$9 n ^ { 2 } + 21 n = 0$$

Whakaoti mō n

$$n = -\frac{7}{3} = -2\frac{1}{3} \approx -2.333333333$$

$$n=0$$

Ngā Upane Whakamahi Tauwehe

Tauwehea te n.

$$n\left(9n+21\right)=0$$

Hei kimi otinga whārite, me whakaoti te n=0 me te 9n+21=0.

$$n=0 n=-\frac{7}{3}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Ko ngā whārite katoa o te āhua ax^{2}+bx+c=0 ka taea te whakaoti mā te whakamahi i te tikanga tātai pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. E rua ngā otinga ka puta i te tikanga tātai pūrua, ko tētahi ina he tāpiri a ±, ā, ko tētahi ina he tango.

$$9n^{2}+21n=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 9 mō a, 21 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$n=\frac{-21±\sqrt{21^{2}}}{2\times 9}$$

Tuhia te pūtakerua o te 21^{2}.

$$n=\frac{-21±21}{2\times 9}$$

Whakareatia 2 ki te 9.

$$n=\frac{-21±21}{18}$$

Nā, me whakaoti te whārite n=\frac{-21±21}{18} ina he tāpiri te ±. Tāpiri -21 ki te 21.

$$n=\frac{0}{18}$$

Whakawehe 0 ki te 18.

$$n=0$$

Nā, me whakaoti te whārite n=\frac{-21±21}{18} ina he tango te ±. Tango 21 mai i -21.

$$n=-\frac{42}{18}$$

Whakahekea te hautanga \frac{-42}{18} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 6.

$$n=-\frac{7}{3}$$

Kua oti te whārite te whakatau.

$$n=0 n=-\frac{7}{3}$$

Ngā Upane mō te Whakaoti i te Pūrua

Ko ngā whārite pūrua pēnei i tēnei nā ka taea te whakaoti mā te whakaoti i te pūrua. Hei whakaoti i te pūrua, ko te whārite me mātua tuhi ki te āhua x^{2}+bx=c.

$$9n^{2}+21n=0$$

Whakawehea ngā taha e rua ki te 9.

$$\frac{9n^{2}+21n}{9}=\frac{0}{9}$$

Mā te whakawehe ki te 9 ka wetekia te whakareanga ki te 9.

$$n^{2}+\frac{21}{9}n=\frac{0}{9}$$

Whakahekea te hautanga \frac{21}{9} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$n^{2}+\frac{7}{3}n=\frac{0}{9}$$

Whakawehe 0 ki te 9.

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

Whakawehea te \frac{7}{3}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{7}{6}. Nā, tāpiria te pūrua o te \frac{7}{6} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$n^{2}+\frac{7}{3}n+\left(\frac{7}{6}\right)^{2}=\left(\frac{7}{6}\right)^{2}$$

Pūruatia \frac{7}{6} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$n^{2}+\frac{7}{3}n+\frac{49}{36}=\frac{49}{36}$$

Tauwehea n^{2}+\frac{7}{3}n+\frac{49}{36}. 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}.

$$\left(n+\frac{7}{6}\right)^{2}=\frac{49}{36}$$

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

$$\sqrt{\left(n+\frac{7}{6}\right)^{2}}=\sqrt{\frac{49}{36}}$$

Whakarūnātia.

$$n+\frac{7}{6}=\frac{7}{6} n+\frac{7}{6}=-\frac{7}{6}$$

Me tango \frac{7}{6} mai i ngā taha e rua o te whārite.

$$n=0 n=-\frac{7}{3}$$