Whakaoti i te -2/j+7=j/5

$$\frac { - 2 } { j + 7 } = \frac { j } { 5 }$$

Whakaoti mō j

$$j=-5$$

$$j=-2$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe j ki -7 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 5\left(j+7\right), arā, te tauraro pātahi he tino iti rawa te kitea o j+7,5.

$$5\left(-2\right)=\left(j+7\right)j$$

Whakareatia te 5 ki te -2, ka -10.

$$-10=\left(j+7\right)j$$

Whakamahia te āhuatanga tohatoha hei whakarea te j+7 ki te j.

$$-10=j^{2}+7j$$

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

$$j^{2}+7j=-10$$

Me tāpiri te 10 ki ngā taha e rua.

$$j^{2}+7j+10=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 7 mō b, me 10 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$j=\frac{-7±\sqrt{7^{2}-4\times 10}}{2}$$

Pūrua 7.

$$j=\frac{-7±\sqrt{49-4\times 10}}{2}$$

Whakareatia -4 ki te 10.

$$j=\frac{-7±\sqrt{49-40}}{2}$$

Tāpiri 49 ki te -40.

$$j=\frac{-7±\sqrt{9}}{2}$$

Tuhia te pūtakerua o te 9.

$$j=\frac{-7±3}{2}$$

Nā, me whakaoti te whārite j=\frac{-7±3}{2} ina he tāpiri te ±. Tāpiri -7 ki te 3.

$$j=-\frac{4}{2}$$

Whakawehe -4 ki te 2.

$$j=-2$$

Nā, me whakaoti te whārite j=\frac{-7±3}{2} ina he tango te ±. Tango 3 mai i -7.

$$j=-\frac{10}{2}$$

Whakawehe -10 ki te 2.

$$j=-5$$

Kua oti te whārite te whakatau.

$$j=-2 j=-5$$

Ngā Upane mō te Whakaoti i te Pūrua

Tē taea kia ōrite te tāupe j ki -7 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 5\left(j+7\right), arā, te tauraro pātahi he tino iti rawa te kitea o j+7,5.

$$5\left(-2\right)=\left(j+7\right)j$$

Whakareatia te 5 ki te -2, ka -10.

$$-10=\left(j+7\right)j$$

Whakamahia te āhuatanga tohatoha hei whakarea te j+7 ki te j.

$$-10=j^{2}+7j$$

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

$$j^{2}+7j=-10$$

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

$$j^{2}+7j+\left(\frac{7}{2}\right)^{2}=-10+\left(\frac{7}{2}\right)^{2}$$

Pūruatia \frac{7}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$j^{2}+7j+\frac{49}{4}=-10+\frac{49}{4}$$

Tāpiri -10 ki te \frac{49}{4}.

$$j^{2}+7j+\frac{49}{4}=\frac{9}{4}$$

Tauwehea j^{2}+7j+\frac{49}{4}. 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}.

$$\left(j+\frac{7}{2}\right)^{2}=\frac{9}{4}$$

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

$$\sqrt{\left(j+\frac{7}{2}\right)^{2}}=\sqrt{\frac{9}{4}}$$

Whakarūnātia.

$$j+\frac{7}{2}=\frac{3}{2} j+\frac{7}{2}=-\frac{3}{2}$$

Me tango \frac{7}{2} mai i ngā taha e rua o te whārite.

$$j=-2 j=-5$$