Whakaoti i te 15=8h^2-2h

$$15 = 8 h ^ { 2 } - 2 h$$

Whakaoti mō h

$$h = \frac{3}{2} = 1\frac{1}{2} = 1.5$$

$$h = -\frac{5}{4} = -1\frac{1}{4} = -1.25$$

Ngā Upane Whakamahi Tauwehe Mā te Whakarōpū

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$8h^{2}-2h=15$$

Tangohia te 15 mai i ngā taha e rua.

$$8h^{2}-2h-15=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei 8h^{2}+ah+bh-15. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-2 ab=8\left(-15\right)=-120$$

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 -120.

$$1,-120 2,-60 3,-40 4,-30 5,-24 6,-20 8,-15 10,-12$$

Tātaihia te tapeke mō ia takirua.

$$1-120=-119 2-60=-58 3-40=-37 4-30=-26 5-24=-19 6-20=-14 8-15=-7 10-12=-2$$

Ko te otinga te takirua ka hoatu i te tapeke -2.

$$a=-12 b=10$$

Tuhia anō te 8h^{2}-2h-15 hei \left(8h^{2}-12h\right)+\left(10h-15\right).

$$\left(8h^{2}-12h\right)+\left(10h-15\right)$$

Tauwehea te 4h i te tuatahi me te 5 i te rōpū tuarua.

$$4h\left(2h-3\right)+5\left(2h-3\right)$$

Whakatauwehea atu te kīanga pātahi 2h-3 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(2h-3\right)\left(4h+5\right)$$

Hei kimi otinga whārite, me whakaoti te 2h-3=0 me te 4h+5=0.

$$h=\frac{3}{2} h=-\frac{5}{4}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$8h^{2}-2h=15$$

Tangohia te 15 mai i ngā taha e rua.

$$8h^{2}-2h-15=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 8 mō a, -2 mō b, me -15 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$h=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\times 8\left(-15\right)}}{2\times 8}$$

Pūrua -2.

$$h=\frac{-\left(-2\right)±\sqrt{4-4\times 8\left(-15\right)}}{2\times 8}$$

Whakareatia -4 ki te 8.

$$h=\frac{-\left(-2\right)±\sqrt{4-32\left(-15\right)}}{2\times 8}$$

Whakareatia -32 ki te -15.

$$h=\frac{-\left(-2\right)±\sqrt{4+480}}{2\times 8}$$

Tāpiri 4 ki te 480.

$$h=\frac{-\left(-2\right)±\sqrt{484}}{2\times 8}$$

Tuhia te pūtakerua o te 484.

$$h=\frac{-\left(-2\right)±22}{2\times 8}$$

Ko te tauaro o -2 ko 2.

$$h=\frac{2±22}{2\times 8}$$

Whakareatia 2 ki te 8.

$$h=\frac{2±22}{16}$$

Nā, me whakaoti te whārite h=\frac{2±22}{16} ina he tāpiri te ±. Tāpiri 2 ki te 22.

$$h=\frac{24}{16}$$

Whakahekea te hautanga \frac{24}{16} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 8.

$$h=\frac{3}{2}$$

Nā, me whakaoti te whārite h=\frac{2±22}{16} ina he tango te ±. Tango 22 mai i 2.

$$h=-\frac{20}{16}$$

Whakahekea te hautanga \frac{-20}{16} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$h=-\frac{5}{4}$$

Kua oti te whārite te whakatau.

$$h=\frac{3}{2} h=-\frac{5}{4}$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$8h^{2}-2h=15$$

Whakawehea ngā taha e rua ki te 8.

$$\frac{8h^{2}-2h}{8}=\frac{15}{8}$$

Mā te whakawehe ki te 8 ka wetekia te whakareanga ki te 8.

$$h^{2}+\left(-\frac{2}{8}\right)h=\frac{15}{8}$$

Whakahekea te hautanga \frac{-2}{8} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$h^{2}-\frac{1}{4}h=\frac{15}{8}$$

Whakawehea te -\frac{1}{4}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{1}{8}. Nā, tāpiria te pūrua o te -\frac{1}{8} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$h^{2}-\frac{1}{4}h+\left(-\frac{1}{8}\right)^{2}=\frac{15}{8}+\left(-\frac{1}{8}\right)^{2}$$

Pūruatia -\frac{1}{8} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$h^{2}-\frac{1}{4}h+\frac{1}{64}=\frac{15}{8}+\frac{1}{64}$$

Tāpiri \frac{15}{8} ki te \frac{1}{64} 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.

$$h^{2}-\frac{1}{4}h+\frac{1}{64}=\frac{121}{64}$$

Tauwehea h^{2}-\frac{1}{4}h+\frac{1}{64}. 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}.

$$\left(h-\frac{1}{8}\right)^{2}=\frac{121}{64}$$

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

$$\sqrt{\left(h-\frac{1}{8}\right)^{2}}=\sqrt{\frac{121}{64}}$$

Whakarūnātia.

$$h-\frac{1}{8}=\frac{11}{8} h-\frac{1}{8}=-\frac{11}{8}$$

Me tāpiri \frac{1}{8} ki ngā taha e rua o te whārite.

$$h=\frac{3}{2} h=-\frac{5}{4}$$