Whakaoti i te 5p^2=35p

$$5 p ^ { 2 } = 35 p$$

Whakaoti mō p

$$p=7$$

$$p=0$$

Ngā Upane Whakamahi Tauwehe

Tangohia te 35p mai i ngā taha e rua.

$$5p^{2}-35p=0$$

Tauwehea te p.

$$p\left(5p-35\right)=0$$

Hei kimi otinga whārite, me whakaoti te p=0 me te 5p-35=0.

$$p=0 p=7$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 35p mai i ngā taha e rua.

$$5p^{2}-35p=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 5 mō a, -35 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$p=\frac{-\left(-35\right)±\sqrt{\left(-35\right)^{2}}}{2\times 5}$$

Tuhia te pūtakerua o te \left(-35\right)^{2}.

$$p=\frac{-\left(-35\right)±35}{2\times 5}$$

Ko te tauaro o -35 ko 35.

$$p=\frac{35±35}{2\times 5}$$

Whakareatia 2 ki te 5.

$$p=\frac{35±35}{10}$$

Nā, me whakaoti te whārite p=\frac{35±35}{10} ina he tāpiri te ±. Tāpiri 35 ki te 35.

$$p=\frac{70}{10}$$

Whakawehe 70 ki te 10.

$$p=7$$

Nā, me whakaoti te whārite p=\frac{35±35}{10} ina he tango te ±. Tango 35 mai i 35.

$$p=\frac{0}{10}$$

Whakawehe 0 ki te 10.

$$p=0$$

Kua oti te whārite te whakatau.

$$p=7 p=0$$

Ngā Upane mō te Whakaoti i te Pūrua

Tangohia te 35p mai i ngā taha e rua.

$$5p^{2}-35p=0$$

Whakawehea ngā taha e rua ki te 5.

$$\frac{5p^{2}-35p}{5}=\frac{0}{5}$$

Mā te whakawehe ki te 5 ka wetekia te whakareanga ki te 5.

$$p^{2}+\left(-\frac{35}{5}\right)p=\frac{0}{5}$$

Whakawehe -35 ki te 5.

$$p^{2}-7p=\frac{0}{5}$$

Whakawehe 0 ki te 5.

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

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

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

Pūruatia -\frac{7}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$p^{2}-7p+\frac{49}{4}=\frac{49}{4}$$

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

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

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

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

Whakarūnātia.

$$p-\frac{7}{2}=\frac{7}{2} p-\frac{7}{2}=-\frac{7}{2}$$

Me tāpiri \frac{7}{2} ki ngā taha e rua o te whārite.

$$p=7 p=0$$