Whakaoti i te 2s^2-7s=0

$$2 s ^ { 2 } - 7 s = 0$$

Whakaoti mō s

$$s = \frac{7}{2} = 3\frac{1}{2} = 3.5$$

$$s=0$$

Ngā Upane Whakamahi Tauwehe

Tauwehea te s.

$$s\left(2s-7\right)=0$$

Hei kimi otinga whārite, me whakaoti te s=0 me te 2s-7=0.

$$s=0 s=\frac{7}{2}$$

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.

$$2s^{2}-7s=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 2 mō a, -7 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$s=\frac{-\left(-7\right)±\sqrt{\left(-7\right)^{2}}}{2\times 2}$$

Tuhia te pūtakerua o te \left(-7\right)^{2}.

$$s=\frac{-\left(-7\right)±7}{2\times 2}$$

Ko te tauaro o -7 ko 7.

$$s=\frac{7±7}{2\times 2}$$

Whakareatia 2 ki te 2.

$$s=\frac{7±7}{4}$$

Nā, me whakaoti te whārite s=\frac{7±7}{4} ina he tāpiri te ±. Tāpiri 7 ki te 7.

$$s=\frac{14}{4}$$

Whakahekea te hautanga \frac{14}{4} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$s=\frac{7}{2}$$

Nā, me whakaoti te whārite s=\frac{7±7}{4} ina he tango te ±. Tango 7 mai i 7.

$$s=\frac{0}{4}$$

Whakawehe 0 ki te 4.

$$s=0$$

Kua oti te whārite te whakatau.

$$s=\frac{7}{2} s=0$$

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.

$$2s^{2}-7s=0$$

Whakawehea ngā taha e rua ki te 2.

$$\frac{2s^{2}-7s}{2}=\frac{0}{2}$$

Mā te whakawehe ki te 2 ka wetekia te whakareanga ki te 2.

$$s^{2}-\frac{7}{2}s=\frac{0}{2}$$

Whakawehe 0 ki te 2.

$$s^{2}-\frac{7}{2}s=0$$

Whakawehea te -\frac{7}{2}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{7}{4}. Nā, tāpiria te pūrua o te -\frac{7}{4} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$s^{2}-\frac{7}{2}s+\left(-\frac{7}{4}\right)^{2}=\left(-\frac{7}{4}\right)^{2}$$

Pūruatia -\frac{7}{4} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$s^{2}-\frac{7}{2}s+\frac{49}{16}=\frac{49}{16}$$

Tauwehea s^{2}-\frac{7}{2}s+\frac{49}{16}. 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}.

$$\left(s-\frac{7}{4}\right)^{2}=\frac{49}{16}$$

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

$$\sqrt{\left(s-\frac{7}{4}\right)^{2}}=\sqrt{\frac{49}{16}}$$

Whakarūnātia.

$$s-\frac{7}{4}=\frac{7}{4} s-\frac{7}{4}=-\frac{7}{4}$$

Me tāpiri \frac{7}{4} ki ngā taha e rua o te whārite.

$$s=\frac{7}{2} s=0$$