Whakaoti i te s^2-9s=0

$$s ^ { 2 } - 9 s = 0$$

Whakaoti mō s

$$s=9$$

$$s=0$$

Ngā Upane Whakamahi Tauwehe

Tauwehea te s.

$$s\left(s-9\right)=0$$

Hei kimi otinga whārite, me whakaoti te s=0 me te s-9=0.

$$s=0 s=9$$

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.

$$s^{2}-9s=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -9 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$s=\frac{-\left(-9\right)±\sqrt{\left(-9\right)^{2}}}{2}$$

Tuhia te pūtakerua o te \left(-9\right)^{2}.

$$s=\frac{-\left(-9\right)±9}{2}$$

Ko te tauaro o -9 ko 9.

$$s=\frac{9±9}{2}$$

Nā, me whakaoti te whārite s=\frac{9±9}{2} ina he tāpiri te ±. Tāpiri 9 ki te 9.

$$s=\frac{18}{2}$$

Whakawehe 18 ki te 2.

$$s=9$$

Nā, me whakaoti te whārite s=\frac{9±9}{2} ina he tango te ±. Tango 9 mai i 9.

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

Whakawehe 0 ki te 2.

$$s=0$$

Kua oti te whārite te whakatau.

$$s=9 s=0$$

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.

$$s^{2}-9s=0$$

Whakawehea te -9, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{9}{2}. Nā, tāpiria te pūrua o te -\frac{9}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$s^{2}-9s+\left(-\frac{9}{2}\right)^{2}=\left(-\frac{9}{2}\right)^{2}$$

Pūruatia -\frac{9}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$s^{2}-9s+\frac{81}{4}=\frac{81}{4}$$

Tauwehea s^{2}-9s+\frac{81}{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}.

$$\left(s-\frac{9}{2}\right)^{2}=\frac{81}{4}$$

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

$$\sqrt{\left(s-\frac{9}{2}\right)^{2}}=\sqrt{\frac{81}{4}}$$

Whakarūnātia.

$$s-\frac{9}{2}=\frac{9}{2} s-\frac{9}{2}=-\frac{9}{2}$$

Me tāpiri \frac{9}{2} ki ngā taha e rua o te whārite.

$$s=9 s=0$$