Whakaoti i te 6p^2-5=13p

$$6 p ^ { 2 } - 5 = 13 p$$

Whakaoti mō p

$$p=-\frac{1}{3}\approx -0.333333333$$

$$p = \frac{5}{2} = 2\frac{1}{2} = 2.5$$

Ngā Upane Whakamahi Tauwehe Mā te Whakarōpū

Tangohia te 13p mai i ngā taha e rua.

$$6p^{2}-5-13p=0$$

Hurinahatia te pūrau ki te āhua tānga ngahuru. Whakaraupapahia ngā kīanga tau mai i te pū teitei rawa ki te mea iti rawa.

$$6p^{2}-13p-5=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei 6p^{2}+ap+bp-5. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-13 ab=6\left(-5\right)=-30$$

I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōraro te a+b, he nui ake te uara pū o te tau tōraro i tō te tōrunga. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua -30.

$$1,-30 2,-15 3,-10 5,-6$$

Tātaihia te tapeke mō ia takirua.

$$1-30=-29 2-15=-13 3-10=-7 5-6=-1$$

Ko te otinga te takirua ka hoatu i te tapeke -13.

$$a=-15 b=2$$

Tuhia anō te 6p^{2}-13p-5 hei \left(6p^{2}-15p\right)+\left(2p-5\right).

$$\left(6p^{2}-15p\right)+\left(2p-5\right)$$

Whakatauwehea atu 3p i te 6p^{2}-15p.

$$3p\left(2p-5\right)+2p-5$$

Whakatauwehea atu te kīanga pātahi 2p-5 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(2p-5\right)\left(3p+1\right)$$

Hei kimi otinga whārite, me whakaoti te 2p-5=0 me te 3p+1=0.

$$p=\frac{5}{2} p=-\frac{1}{3}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 13p mai i ngā taha e rua.

$$6p^{2}-5-13p=0$$

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.

$$6p^{2}-13p-5=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 6 mō a, -13 mō b, me -5 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$p=\frac{-\left(-13\right)±\sqrt{\left(-13\right)^{2}-4\times 6\left(-5\right)}}{2\times 6}$$

Pūrua -13.

$$p=\frac{-\left(-13\right)±\sqrt{169-4\times 6\left(-5\right)}}{2\times 6}$$

Whakareatia -4 ki te 6.

$$p=\frac{-\left(-13\right)±\sqrt{169-24\left(-5\right)}}{2\times 6}$$

Whakareatia -24 ki te -5.

$$p=\frac{-\left(-13\right)±\sqrt{169+120}}{2\times 6}$$

Tāpiri 169 ki te 120.

$$p=\frac{-\left(-13\right)±\sqrt{289}}{2\times 6}$$

Tuhia te pūtakerua o te 289.

$$p=\frac{-\left(-13\right)±17}{2\times 6}$$

Ko te tauaro o -13 ko 13.

$$p=\frac{13±17}{2\times 6}$$

Whakareatia 2 ki te 6.

$$p=\frac{13±17}{12}$$

Nā, me whakaoti te whārite p=\frac{13±17}{12} ina he tāpiri te ±. Tāpiri 13 ki te 17.

$$p=\frac{30}{12}$$

Whakahekea te hautanga \frac{30}{12} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 6.

$$p=\frac{5}{2}$$

Nā, me whakaoti te whārite p=\frac{13±17}{12} ina he tango te ±. Tango 17 mai i 13.

$$p=-\frac{4}{12}$$

Whakahekea te hautanga \frac{-4}{12} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$p=-\frac{1}{3}$$

Kua oti te whārite te whakatau.

$$p=\frac{5}{2} p=-\frac{1}{3}$$

Ngā Upane mō te Whakaoti i te Pūrua

Tangohia te 13p mai i ngā taha e rua.

$$6p^{2}-5-13p=0$$

Me tāpiri te 5 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$6p^{2}-13p=5$$

Whakawehea ngā taha e rua ki te 6.

$$\frac{6p^{2}-13p}{6}=\frac{5}{6}$$

Mā te whakawehe ki te 6 ka wetekia te whakareanga ki te 6.

$$p^{2}-\frac{13}{6}p=\frac{5}{6}$$

Whakawehea te -\frac{13}{6}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{13}{12}. Nā, tāpiria te pūrua o te -\frac{13}{12} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$p^{2}-\frac{13}{6}p+\left(-\frac{13}{12}\right)^{2}=\frac{5}{6}+\left(-\frac{13}{12}\right)^{2}$$

Pūruatia -\frac{13}{12} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$p^{2}-\frac{13}{6}p+\frac{169}{144}=\frac{5}{6}+\frac{169}{144}$$

Tāpiri \frac{5}{6} ki te \frac{169}{144} mā te kimi i te tauraro pātahi me te tāpiri i ngā taurunga. Ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$p^{2}-\frac{13}{6}p+\frac{169}{144}=\frac{289}{144}$$

Tauwehea p^{2}-\frac{13}{6}p+\frac{169}{144}. 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}.

$$\left(p-\frac{13}{12}\right)^{2}=\frac{289}{144}$$

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

$$\sqrt{\left(p-\frac{13}{12}\right)^{2}}=\sqrt{\frac{289}{144}}$$

Whakarūnātia.

$$p-\frac{13}{12}=\frac{17}{12} p-\frac{13}{12}=-\frac{17}{12}$$

Me tāpiri \frac{13}{12} ki ngā taha e rua o te whārite.

$$p=\frac{5}{2} p=-\frac{1}{3}$$