Whakaoti i te 3u^2=-15u

$$3 u ^ { 2 } = - 15 u$$

Whakaoti mō u

$$u=-5$$

$$u=0$$

Ngā Upane Whakamahi Tauwehe

Me tāpiri te 15u ki ngā taha e rua.

$$3u^{2}+15u=0$$

Tauwehea te u.

$$u\left(3u+15\right)=0$$

Hei kimi otinga whārite, me whakaoti te u=0 me te 3u+15=0.

$$u=0 u=-5$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Me tāpiri te 15u ki ngā taha e rua.

$$3u^{2}+15u=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 3 mō a, 15 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$u=\frac{-15±\sqrt{15^{2}}}{2\times 3}$$

Tuhia te pūtakerua o te 15^{2}.

$$u=\frac{-15±15}{2\times 3}$$

Whakareatia 2 ki te 3.

$$u=\frac{-15±15}{6}$$

Nā, me whakaoti te whārite u=\frac{-15±15}{6} ina he tāpiri te ±. Tāpiri -15 ki te 15.

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

Whakawehe 0 ki te 6.

$$u=0$$

Nā, me whakaoti te whārite u=\frac{-15±15}{6} ina he tango te ±. Tango 15 mai i -15.

$$u=-\frac{30}{6}$$

Whakawehe -30 ki te 6.

$$u=-5$$

Kua oti te whārite te whakatau.

$$u=0 u=-5$$

Ngā Upane mō te Whakaoti i te Pūrua

Me tāpiri te 15u ki ngā taha e rua.

$$3u^{2}+15u=0$$

Whakawehea ngā taha e rua ki te 3.

$$\frac{3u^{2}+15u}{3}=\frac{0}{3}$$

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

$$u^{2}+\frac{15}{3}u=\frac{0}{3}$$

Whakawehe 15 ki te 3.

$$u^{2}+5u=\frac{0}{3}$$

Whakawehe 0 ki te 3.

$$u^{2}+5u=0$$

Whakawehea te 5, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{5}{2}. Nā, tāpiria te pūrua o te \frac{5}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$u^{2}+5u+\left(\frac{5}{2}\right)^{2}=\left(\frac{5}{2}\right)^{2}$$

Pūruatia \frac{5}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$u^{2}+5u+\frac{25}{4}=\frac{25}{4}$$

Tauwehea u^{2}+5u+\frac{25}{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}.

$$\left(u+\frac{5}{2}\right)^{2}=\frac{25}{4}$$

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

$$\sqrt{\left(u+\frac{5}{2}\right)^{2}}=\sqrt{\frac{25}{4}}$$

Whakarūnātia.

$$u+\frac{5}{2}=\frac{5}{2} u+\frac{5}{2}=-\frac{5}{2}$$

Me tango \frac{5}{2} mai i ngā taha e rua o te whārite.

$$u=0 u=-5$$