Whakaoti i te v/12=-4/v+14

$$\frac { v } { 12 } = \frac { - 4 } { v + 14 }$$

Whakaoti mō v

$$v=-8$$

$$v=-6$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe v ki -14 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 12\left(v+14\right), arā, te tauraro pātahi he tino iti rawa te kitea o 12,v+14.

$$\left(v+14\right)v=12\left(-4\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te v+14 ki te v.

$$v^{2}+14v=12\left(-4\right)$$

Whakareatia te 12 ki te -4, ka -48.

$$v^{2}+14v=-48$$

Me tāpiri te 48 ki ngā taha e rua.

$$v^{2}+14v+48=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 14 mō b, me 48 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$v=\frac{-14±\sqrt{14^{2}-4\times 48}}{2}$$

Pūrua 14.

$$v=\frac{-14±\sqrt{196-4\times 48}}{2}$$

Whakareatia -4 ki te 48.

$$v=\frac{-14±\sqrt{196-192}}{2}$$

Tāpiri 196 ki te -192.

$$v=\frac{-14±\sqrt{4}}{2}$$

Tuhia te pūtakerua o te 4.

$$v=\frac{-14±2}{2}$$

Nā, me whakaoti te whārite v=\frac{-14±2}{2} ina he tāpiri te ±. Tāpiri -14 ki te 2.

$$v=-\frac{12}{2}$$

Whakawehe -12 ki te 2.

$$v=-6$$

Nā, me whakaoti te whārite v=\frac{-14±2}{2} ina he tango te ±. Tango 2 mai i -14.

$$v=-\frac{16}{2}$$

Whakawehe -16 ki te 2.

$$v=-8$$

Kua oti te whārite te whakatau.

$$v=-6 v=-8$$

Ngā Upane mō te Whakaoti i te Pūrua

Tē taea kia ōrite te tāupe v ki -14 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 12\left(v+14\right), arā, te tauraro pātahi he tino iti rawa te kitea o 12,v+14.

$$\left(v+14\right)v=12\left(-4\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te v+14 ki te v.

$$v^{2}+14v=12\left(-4\right)$$

Whakareatia te 12 ki te -4, ka -48.

$$v^{2}+14v=-48$$

Whakawehea te 14, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 7. Nā, tāpiria te pūrua o te 7 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$v^{2}+14v+7^{2}=-48+7^{2}$$

Pūrua 7.

$$v^{2}+14v+49=-48+49$$

Tāpiri -48 ki te 49.

$$v^{2}+14v+49=1$$

Tauwehea v^{2}+14v+49. 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}.

$$\left(v+7\right)^{2}=1$$

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

$$\sqrt{\left(v+7\right)^{2}}=\sqrt{1}$$

Whakarūnātia.

$$v+7=1 v+7=-1$$

Me tango 7 mai i ngā taha e rua o te whārite.

$$v=-6 v=-8$$