Whakaoti i te x+9/20x=27/20

$$x+ \frac{ 9 }{ 20x } = \frac{ 27 }{ 20 }$$

Whakaoti mō x

$$x=\frac{3}{5}=0.6$$

$$x=\frac{3}{4}=0.75$$

Ngā Upane Whakamahi Tauwehe Mā te Whakarōpū

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 20x, arā, te tauraro pātahi he tino iti rawa te kitea o 20x,20.

$$20xx+9=27x$$

Whakareatia te x ki te x, ka x^{2}.

$$20x^{2}+9=27x$$

Tangohia te 27x mai i ngā taha e rua.

$$20x^{2}+9-27x=0$$

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

$$20x^{2}-27x+9=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei 20x^{2}+ax+bx+9. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-27 ab=20\times 9=180$$

I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōraro te a+b, he tōraro hoki a a me b. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 180.

$$-1,-180 -2,-90 -3,-60 -4,-45 -5,-36 -6,-30 -9,-20 -10,-18 -12,-15$$

Tātaihia te tapeke mō ia takirua.

$$-1-180=-181 -2-90=-92 -3-60=-63 -4-45=-49 -5-36=-41 -6-30=-36 -9-20=-29 -10-18=-28 -12-15=-27$$

Ko te otinga te takirua ka hoatu i te tapeke -27.

$$a=-15 b=-12$$

Tuhia anō te 20x^{2}-27x+9 hei \left(20x^{2}-15x\right)+\left(-12x+9\right).

$$\left(20x^{2}-15x\right)+\left(-12x+9\right)$$

Tauwehea te 5x i te tuatahi me te -3 i te rōpū tuarua.

$$5x\left(4x-3\right)-3\left(4x-3\right)$$

Whakatauwehea atu te kīanga pātahi 4x-3 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(4x-3\right)\left(5x-3\right)$$

Hei kimi otinga whārite, me whakaoti te 4x-3=0 me te 5x-3=0.

$$x=\frac{3}{4} x=\frac{3}{5}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 20x, arā, te tauraro pātahi he tino iti rawa te kitea o 20x,20.

$$20xx+9=27x$$

Whakareatia te x ki te x, ka x^{2}.

$$20x^{2}+9=27x$$

Tangohia te 27x mai i ngā taha e rua.

$$20x^{2}+9-27x=0$$

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.

$$20x^{2}-27x+9=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 20 mō a, -27 mō b, me 9 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-27\right)±\sqrt{\left(-27\right)^{2}-4\times 20\times 9}}{2\times 20}$$

Pūrua -27.

$$x=\frac{-\left(-27\right)±\sqrt{729-4\times 20\times 9}}{2\times 20}$$

Whakareatia -4 ki te 20.

$$x=\frac{-\left(-27\right)±\sqrt{729-80\times 9}}{2\times 20}$$

Whakareatia -80 ki te 9.

$$x=\frac{-\left(-27\right)±\sqrt{729-720}}{2\times 20}$$

Tāpiri 729 ki te -720.

$$x=\frac{-\left(-27\right)±\sqrt{9}}{2\times 20}$$

Tuhia te pūtakerua o te 9.

$$x=\frac{-\left(-27\right)±3}{2\times 20}$$

Ko te tauaro o -27 ko 27.

$$x=\frac{27±3}{2\times 20}$$

Whakareatia 2 ki te 20.

$$x=\frac{27±3}{40}$$

Nā, me whakaoti te whārite x=\frac{27±3}{40} ina he tāpiri te ±. Tāpiri 27 ki te 3.

$$x=\frac{30}{40}$$

Whakahekea te hautanga \frac{30}{40} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 10.

$$x=\frac{3}{4}$$

Nā, me whakaoti te whārite x=\frac{27±3}{40} ina he tango te ±. Tango 3 mai i 27.

$$x=\frac{24}{40}$$

Whakahekea te hautanga \frac{24}{40} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 8.

$$x=\frac{3}{5}$$

Kua oti te whārite te whakatau.

$$x=\frac{3}{4} x=\frac{3}{5}$$

Ngā Upane mō te Whakaoti i te Pūrua

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 20x, arā, te tauraro pātahi he tino iti rawa te kitea o 20x,20.

$$20xx+9=27x$$

Whakareatia te x ki te x, ka x^{2}.

$$20x^{2}+9=27x$$

Tangohia te 27x mai i ngā taha e rua.

$$20x^{2}+9-27x=0$$

Tangohia te 9 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$20x^{2}-27x=-9$$

Whakawehea ngā taha e rua ki te 20.

$$\frac{20x^{2}-27x}{20}=-\frac{9}{20}$$

Mā te whakawehe ki te 20 ka wetekia te whakareanga ki te 20.

$$x^{2}-\frac{27}{20}x=-\frac{9}{20}$$

Whakawehea te -\frac{27}{20}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{27}{40}. Nā, tāpiria te pūrua o te -\frac{27}{40} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{27}{20}x+\left(-\frac{27}{40}\right)^{2}=-\frac{9}{20}+\left(-\frac{27}{40}\right)^{2}$$

Pūruatia -\frac{27}{40} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{27}{20}x+\frac{729}{1600}=-\frac{9}{20}+\frac{729}{1600}$$

Tāpiri -\frac{9}{20} ki te \frac{729}{1600} 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.

$$x^{2}-\frac{27}{20}x+\frac{729}{1600}=\frac{9}{1600}$$

Tauwehea x^{2}-\frac{27}{20}x+\frac{729}{1600}. 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}.

$$\left(x-\frac{27}{40}\right)^{2}=\frac{9}{1600}$$

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

$$\sqrt{\left(x-\frac{27}{40}\right)^{2}}=\sqrt{\frac{9}{1600}}$$

Whakarūnātia.

$$x-\frac{27}{40}=\frac{3}{40} x-\frac{27}{40}=-\frac{3}{40}$$

Me tāpiri \frac{27}{40} ki ngā taha e rua o te whārite.

$$x=\frac{3}{4} x=\frac{3}{5}$$