Whakaoti i te 64+(n-1)*2/n*n=858

$$\frac { 64 + ( n - 1 ) \cdot 2 } { n } \cdot n = 858$$

Whakaoti mō n

$$n=398$$

Ngā Upane Whakamahi Tauwehe

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

$$\left(64+\left(n-1\right)\times 2\right)n=858n$$

Whakamahia te āhuatanga tohatoha hei whakarea te n-1 ki te 2.

$$\left(64+2n-2\right)n=858n$$

Tangohia te 2 i te 64, ka 62.

$$\left(62+2n\right)n=858n$$

Whakamahia te āhuatanga tohatoha hei whakarea te 62+2n ki te n.

$$62n+2n^{2}=858n$$

Tangohia te 858n mai i ngā taha e rua.

$$62n+2n^{2}-858n=0$$

Pahekotia te 62n me -858n, ka -796n.

$$-796n+2n^{2}=0$$

Tauwehea te n.

$$n\left(-796+2n\right)=0$$

Hei kimi otinga whārite, me whakaoti te n=0 me te -796+2n=0.

$$n=0 n=398$$

Tē taea kia ōrite te tāupe n ki 0.

$$n=398$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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

$$\left(64+\left(n-1\right)\times 2\right)n=858n$$

Whakamahia te āhuatanga tohatoha hei whakarea te n-1 ki te 2.

$$\left(64+2n-2\right)n=858n$$

Tangohia te 2 i te 64, ka 62.

$$\left(62+2n\right)n=858n$$

Whakamahia te āhuatanga tohatoha hei whakarea te 62+2n ki te n.

$$62n+2n^{2}=858n$$

Tangohia te 858n mai i ngā taha e rua.

$$62n+2n^{2}-858n=0$$

Pahekotia te 62n me -858n, ka -796n.

$$-796n+2n^{2}=0$$

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.

$$2n^{2}-796n=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 2 mō a, -796 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$n=\frac{-\left(-796\right)±\sqrt{\left(-796\right)^{2}}}{2\times 2}$$

Tuhia te pūtakerua o te \left(-796\right)^{2}.

$$n=\frac{-\left(-796\right)±796}{2\times 2}$$

Ko te tauaro o -796 ko 796.

$$n=\frac{796±796}{2\times 2}$$

Whakareatia 2 ki te 2.

$$n=\frac{796±796}{4}$$

Nā, me whakaoti te whārite n=\frac{796±796}{4} ina he tāpiri te ±. Tāpiri 796 ki te 796.

$$n=\frac{1592}{4}$$

Whakawehe 1592 ki te 4.

$$n=398$$

Nā, me whakaoti te whārite n=\frac{796±796}{4} ina he tango te ±. Tango 796 mai i 796.

$$n=\frac{0}{4}$$

Whakawehe 0 ki te 4.

$$n=0$$

Kua oti te whārite te whakatau.

$$n=398 n=0$$

Tē taea kia ōrite te tāupe n ki 0.

$$n=398$$

Ngā Upane mō te Whakaoti i te Pūrua

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

$$\left(64+\left(n-1\right)\times 2\right)n=858n$$

Whakamahia te āhuatanga tohatoha hei whakarea te n-1 ki te 2.

$$\left(64+2n-2\right)n=858n$$

Tangohia te 2 i te 64, ka 62.

$$\left(62+2n\right)n=858n$$

Whakamahia te āhuatanga tohatoha hei whakarea te 62+2n ki te n.

$$62n+2n^{2}=858n$$

Tangohia te 858n mai i ngā taha e rua.

$$62n+2n^{2}-858n=0$$

Pahekotia te 62n me -858n, ka -796n.

$$-796n+2n^{2}=0$$

Ko ngā whārite pūrua pēnei i tēnei nā ka taea te whakaoti mā te whakaoti i te pūrua. Hei whakaoti i te pūrua, ko te whārite me mātua tuhi ki te āhua x^{2}+bx=c.

$$2n^{2}-796n=0$$

Whakawehea ngā taha e rua ki te 2.

$$\frac{2n^{2}-796n}{2}=\frac{0}{2}$$

Mā te whakawehe ki te 2 ka wetekia te whakareanga ki te 2.

$$n^{2}+\left(-\frac{796}{2}\right)n=\frac{0}{2}$$

Whakawehe -796 ki te 2.

$$n^{2}-398n=\frac{0}{2}$$

Whakawehe 0 ki te 2.

$$n^{2}-398n=0$$

Whakawehea te -398, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -199. Nā, tāpiria te pūrua o te -199 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$n^{2}-398n+\left(-199\right)^{2}=\left(-199\right)^{2}$$

Pūrua -199.

$$n^{2}-398n+39601=39601$$

Tauwehea n^{2}-398n+39601. 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}.

$$\left(n-199\right)^{2}=39601$$

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

$$\sqrt{\left(n-199\right)^{2}}=\sqrt{39601}$$

Whakarūnātia.

$$n-199=199 n-199=-199$$

Me tāpiri 199 ki ngā taha e rua o te whārite.

$$n=398 n=0$$

Tē taea kia ōrite te tāupe n ki 0.

$$n=398$$