Whakaoti i te 1/w=w+2/35

$$\frac { 1 } { w } = \frac { w + 2 } { 35 }$$

Whakaoti mō w

$$w=-7$$

$$w=5$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe w ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 35w, arā, te tauraro pātahi he tino iti rawa te kitea o w,35.

$$35=w\left(w+2\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te w ki te w+2.

$$35=w^{2}+2w$$

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

$$w^{2}+2w=35$$

Tangohia te 35 mai i ngā taha e rua.

$$w^{2}+2w-35=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 2 mō b, me -35 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$w=\frac{-2±\sqrt{2^{2}-4\left(-35\right)}}{2}$$

Pūrua 2.

$$w=\frac{-2±\sqrt{4-4\left(-35\right)}}{2}$$

Whakareatia -4 ki te -35.

$$w=\frac{-2±\sqrt{4+140}}{2}$$

Tāpiri 4 ki te 140.

$$w=\frac{-2±\sqrt{144}}{2}$$

Tuhia te pūtakerua o te 144.

$$w=\frac{-2±12}{2}$$

Nā, me whakaoti te whārite w=\frac{-2±12}{2} ina he tāpiri te ±. Tāpiri -2 ki te 12.

$$w=\frac{10}{2}$$

Whakawehe 10 ki te 2.

$$w=5$$

Nā, me whakaoti te whārite w=\frac{-2±12}{2} ina he tango te ±. Tango 12 mai i -2.

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

Whakawehe -14 ki te 2.

$$w=-7$$

Kua oti te whārite te whakatau.

$$w=5 w=-7$$

Ngā Upane mō te Whakaoti i te Pūrua

Tē taea kia ōrite te tāupe w ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 35w, arā, te tauraro pātahi he tino iti rawa te kitea o w,35.

$$35=w\left(w+2\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te w ki te w+2.

$$35=w^{2}+2w$$

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

$$w^{2}+2w=35$$

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

$$w^{2}+2w+1^{2}=35+1^{2}$$

Pūrua 1.

$$w^{2}+2w+1=35+1$$

Tāpiri 35 ki te 1.

$$w^{2}+2w+1=36$$

Tauwehea w^{2}+2w+1. 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}.

$$\left(w+1\right)^{2}=36$$

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

$$\sqrt{\left(w+1\right)^{2}}=\sqrt{36}$$

Whakarūnātia.

$$w+1=6 w+1=-6$$

Me tango 1 mai i ngā taha e rua o te whārite.

$$w=5 w=-7$$