Whakaoti i te d=7-6d/d

$$d = \frac { 7 - 6 d } { d }$$

Whakaoti mō d

$$d=-7$$

$$d=1$$

Ngā Upane Whakamahi Tauwehe

Tangohia te \frac{7-6d}{d} mai i ngā taha e rua.

$$d-\frac{7-6d}{d}=0$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia d ki te \frac{d}{d}.

$$\frac{dd}{d}-\frac{7-6d}{d}=0$$

Tā te mea he rite te tauraro o \frac{dd}{d} me \frac{7-6d}{d}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{dd-\left(7-6d\right)}{d}=0$$

Mahia ngā whakarea i roto o dd-\left(7-6d\right).

$$\frac{d^{2}-7+6d}{d}=0$$

Tē taea kia ōrite te tāupe d ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te d.

$$d^{2}-7+6d=0$$

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

$$d^{2}+6d-7=0$$

Hei whakaoti i te whārite, whakatauwehea te d^{2}+6d-7 mā te whakamahi i te tātai d^{2}+\left(a+b\right)d+ab=\left(d+a\right)\left(d+b\right). Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=6 ab=-7$$

I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōrunga te a+b, he nui ake te uara pū o te tau tōrunga i tō te tōraro. Ko te takirua anake pērā ko te otinga pūnaha.

$$a=-1 b=7$$

Me tuhi anō te kīanga whakatauwehe \left(d+a\right)\left(d+b\right) mā ngā uara i tātaihia.

$$\left(d-1\right)\left(d+7\right)$$

Hei kimi otinga whārite, me whakaoti te d-1=0 me te d+7=0.

$$d=1 d=-7$$

Ngā Upane Whakamahi Tauwehe Mā te Whakarōpū

Tangohia te \frac{7-6d}{d} mai i ngā taha e rua.

$$d-\frac{7-6d}{d}=0$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia d ki te \frac{d}{d}.

$$\frac{dd}{d}-\frac{7-6d}{d}=0$$

Tā te mea he rite te tauraro o \frac{dd}{d} me \frac{7-6d}{d}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{dd-\left(7-6d\right)}{d}=0$$

Mahia ngā whakarea i roto o dd-\left(7-6d\right).

$$\frac{d^{2}-7+6d}{d}=0$$

Tē taea kia ōrite te tāupe d ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te d.

$$d^{2}-7+6d=0$$

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

$$d^{2}+6d-7=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei d^{2}+ad+bd-7. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=6 ab=1\left(-7\right)=-7$$

I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōrunga te a+b, he nui ake te uara pū o te tau tōrunga i tō te tōraro. Ko te takirua anake pērā ko te otinga pūnaha.

$$a=-1 b=7$$

Tuhia anō te d^{2}+6d-7 hei \left(d^{2}-d\right)+\left(7d-7\right).

$$\left(d^{2}-d\right)+\left(7d-7\right)$$

Tauwehea te d i te tuatahi me te 7 i te rōpū tuarua.

$$d\left(d-1\right)+7\left(d-1\right)$$

Whakatauwehea atu te kīanga pātahi d-1 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(d-1\right)\left(d+7\right)$$

Hei kimi otinga whārite, me whakaoti te d-1=0 me te d+7=0.

$$d=1 d=-7$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te \frac{7-6d}{d} mai i ngā taha e rua.

$$d-\frac{7-6d}{d}=0$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia d ki te \frac{d}{d}.

$$\frac{dd}{d}-\frac{7-6d}{d}=0$$

Tā te mea he rite te tauraro o \frac{dd}{d} me \frac{7-6d}{d}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{dd-\left(7-6d\right)}{d}=0$$

Mahia ngā whakarea i roto o dd-\left(7-6d\right).

$$\frac{d^{2}-7+6d}{d}=0$$

Tē taea kia ōrite te tāupe d ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te d.

$$d^{2}-7+6d=0$$

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.

$$d^{2}+6d-7=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 6 mō b, me -7 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$d=\frac{-6±\sqrt{6^{2}-4\left(-7\right)}}{2}$$

Pūrua 6.

$$d=\frac{-6±\sqrt{36-4\left(-7\right)}}{2}$$

Whakareatia -4 ki te -7.

$$d=\frac{-6±\sqrt{36+28}}{2}$$

Tāpiri 36 ki te 28.

$$d=\frac{-6±\sqrt{64}}{2}$$

Tuhia te pūtakerua o te 64.

$$d=\frac{-6±8}{2}$$

Nā, me whakaoti te whārite d=\frac{-6±8}{2} ina he tāpiri te ±. Tāpiri -6 ki te 8.

$$d=\frac{2}{2}$$

Whakawehe 2 ki te 2.

$$d=1$$

Nā, me whakaoti te whārite d=\frac{-6±8}{2} ina he tango te ±. Tango 8 mai i -6.

$$d=-\frac{14}{2}$$

Whakawehe -14 ki te 2.

$$d=-7$$

Kua oti te whārite te whakatau.

$$d=1 d=-7$$

Ngā Upane mō te Whakaoti i te Pūrua

Tangohia te \frac{7-6d}{d} mai i ngā taha e rua.

$$d-\frac{7-6d}{d}=0$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia d ki te \frac{d}{d}.

$$\frac{dd}{d}-\frac{7-6d}{d}=0$$

Tā te mea he rite te tauraro o \frac{dd}{d} me \frac{7-6d}{d}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{dd-\left(7-6d\right)}{d}=0$$

Mahia ngā whakarea i roto o dd-\left(7-6d\right).

$$\frac{d^{2}-7+6d}{d}=0$$

Tē taea kia ōrite te tāupe d ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te d.

$$d^{2}-7+6d=0$$

Me tāpiri te 7 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$d^{2}+6d=7$$

Whakawehea te 6, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 3. Nā, tāpiria te pūrua o te 3 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$d^{2}+6d+3^{2}=7+3^{2}$$

Pūrua 3.

$$d^{2}+6d+9=7+9$$

Tāpiri 7 ki te 9.

$$d^{2}+6d+9=16$$

Tauwehea d^{2}+6d+9. 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}.

$$\left(d+3\right)^{2}=16$$

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

$$\sqrt{\left(d+3\right)^{2}}=\sqrt{16}$$

Whakarūnātia.

$$d+3=4 d+3=-4$$

Me tango 3 mai i ngā taha e rua o te whārite.

$$d=1 d=-7$$