Whakaoti i te 2p^2-3p-18=0

$$2 p ^ { 2 } - 3 p - 18 = 0$$

Whakaoti mō p

$$p = \frac{3 \sqrt{17} + 3}{4} \approx 3.842329219$$

$$p=\frac{3-3\sqrt{17}}{4}\approx -2.342329219$$

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.

$$2p^{2}-3p-18=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 2 mō a, -3 mō b, me -18 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$p=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}-4\times 2\left(-18\right)}}{2\times 2}$$

Pūrua -3.

$$p=\frac{-\left(-3\right)±\sqrt{9-4\times 2\left(-18\right)}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$p=\frac{-\left(-3\right)±\sqrt{9-8\left(-18\right)}}{2\times 2}$$

Whakareatia -8 ki te -18.

$$p=\frac{-\left(-3\right)±\sqrt{9+144}}{2\times 2}$$

Tāpiri 9 ki te 144.

$$p=\frac{-\left(-3\right)±\sqrt{153}}{2\times 2}$$

Tuhia te pūtakerua o te 153.

$$p=\frac{-\left(-3\right)±3\sqrt{17}}{2\times 2}$$

Ko te tauaro o -3 ko 3.

$$p=\frac{3±3\sqrt{17}}{2\times 2}$$

Whakareatia 2 ki te 2.

$$p=\frac{3±3\sqrt{17}}{4}$$

Nā, me whakaoti te whārite p=\frac{3±3\sqrt{17}}{4} ina he tāpiri te ±. Tāpiri 3 ki te 3\sqrt{17}.

$$p=\frac{3\sqrt{17}+3}{4}$$

Nā, me whakaoti te whārite p=\frac{3±3\sqrt{17}}{4} ina he tango te ±. Tango 3\sqrt{17} mai i 3.

$$p=\frac{3-3\sqrt{17}}{4}$$

Kua oti te whārite te whakatau.

$$p=\frac{3\sqrt{17}+3}{4} p=\frac{3-3\sqrt{17}}{4}$$

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.

$$2p^{2}-3p-18=0$$

Me tāpiri 18 ki ngā taha e rua o te whārite.

$$2p^{2}-3p-18-\left(-18\right)=-\left(-18\right)$$

Mā te tango i te -18 i a ia ake anō ka toe ko te 0.

$$2p^{2}-3p=-\left(-18\right)$$

Tango -18 mai i 0.

$$2p^{2}-3p=18$$

Whakawehea ngā taha e rua ki te 2.

$$\frac{2p^{2}-3p}{2}=\frac{18}{2}$$

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

$$p^{2}-\frac{3}{2}p=\frac{18}{2}$$

Whakawehe 18 ki te 2.

$$p^{2}-\frac{3}{2}p=9$$

Whakawehea te -\frac{3}{2}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{3}{4}. Nā, tāpiria te pūrua o te -\frac{3}{4} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$p^{2}-\frac{3}{2}p+\left(-\frac{3}{4}\right)^{2}=9+\left(-\frac{3}{4}\right)^{2}$$

Pūruatia -\frac{3}{4} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$p^{2}-\frac{3}{2}p+\frac{9}{16}=9+\frac{9}{16}$$

Tāpiri 9 ki te \frac{9}{16}.

$$p^{2}-\frac{3}{2}p+\frac{9}{16}=\frac{153}{16}$$

Tauwehea p^{2}-\frac{3}{2}p+\frac{9}{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}.

$$\left(p-\frac{3}{4}\right)^{2}=\frac{153}{16}$$

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

$$\sqrt{\left(p-\frac{3}{4}\right)^{2}}=\sqrt{\frac{153}{16}}$$

Whakarūnātia.

$$p-\frac{3}{4}=\frac{3\sqrt{17}}{4} p-\frac{3}{4}=-\frac{3\sqrt{17}}{4}$$

Me tāpiri \frac{3}{4} ki ngā taha e rua o te whārite.

$$p=\frac{3\sqrt{17}+3}{4} p=\frac{3-3\sqrt{17}}{4}$$