Whakaoti i te 5/x=-x/3

$$\frac { 5 } { x } = - \frac { x } { 3 }$$

Whakaoti mō x (complex solution)

$$x=-\sqrt{15}i\approx -0-3.872983346i$$

$$x=\sqrt{15}i\approx 3.872983346i$$

Ngā Upane mā te Kimi Pūtakerua

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 3x, arā, te tauraro pātahi he tino iti rawa te kitea o x,3.

$$3\times 5=-xx$$

Whakareatia te x ki te x, ka x^{2}.

$$3\times 5=-x^{2}$$

Whakareatia te 3 ki te 5, ka 15.

$$15=-x^{2}$$

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

$$-x^{2}=15$$

Whakawehea ngā taha e rua ki te -1.

$$x^{2}=-15$$

Kua oti te whārite te whakatau.

$$x=\sqrt{15}i x=-\sqrt{15}i$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 3x, arā, te tauraro pātahi he tino iti rawa te kitea o x,3.

$$3\times 5=-xx$$

Whakareatia te x ki te x, ka x^{2}.

$$3\times 5=-x^{2}$$

Whakareatia te 3 ki te 5, ka 15.

$$15=-x^{2}$$

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

$$-x^{2}=15$$

Tangohia te 15 mai i ngā taha e rua.

$$-x^{2}-15=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -1 mō a, 0 mō b, me -15 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)\left(-15\right)}}{2\left(-1\right)}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\left(-1\right)\left(-15\right)}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$x=\frac{0±\sqrt{4\left(-15\right)}}{2\left(-1\right)}$$

Whakareatia 4 ki te -15.

$$x=\frac{0±\sqrt{-60}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te -60.

$$x=\frac{0±2\sqrt{15}i}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{0±2\sqrt{15}i}{-2}$$

Nā, me whakaoti te whārite x=\frac{0±2\sqrt{15}i}{-2} ina he tāpiri te ±.

$$x=-\sqrt{15}i$$

Nā, me whakaoti te whārite x=\frac{0±2\sqrt{15}i}{-2} ina he tango te ±.

$$x=\sqrt{15}i$$

Kua oti te whārite te whakatau.

$$x=-\sqrt{15}i x=\sqrt{15}i$$