Whakaoti i te 28x=-67.2/x

$$28x= \frac{ -67.2 }{ x }$$

Whakaoti mō x (complex solution)

$$x=-\frac{i\times 2\sqrt{15}}{5}\approx -0-1.549193338i$$

$$x=\frac{i\times 2\sqrt{15}}{5}\approx 1.549193338i$$

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. Whakareatia ngā taha e rua o te whārite ki te x.

$$28xx=-67.2$$

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

$$28x^{2}=-67.2$$

Whakawehea ngā taha e rua ki te 28.

$$x^{2}=\frac{-67.2}{28}$$

Whakarohaina te \frac{-67.2}{28} mā te whakarea i te taurunga me te tauraro ki te 10.

$$x^{2}=\frac{-672}{280}$$

Whakahekea te hautanga \frac{-672}{280} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 56.

$$x^{2}=-\frac{12}{5}$$

Kua oti te whārite te whakatau.

$$x=\frac{2\sqrt{15}i}{5} x=-\frac{2\sqrt{15}i}{5}$$

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. Whakareatia ngā taha e rua o te whārite ki te x.

$$28xx=-67.2$$

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

$$28x^{2}=-67.2$$

Me tāpiri te 67.2 ki ngā taha e rua.

$$28x^{2}+67.2=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 28 mō a, 0 mō b, me 67.2 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 28\times 67.2}}{2\times 28}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 28\times 67.2}}{2\times 28}$$

Whakareatia -4 ki te 28.

$$x=\frac{0±\sqrt{-112\times 67.2}}{2\times 28}$$

Whakareatia -112 ki te 67.2.

$$x=\frac{0±\sqrt{-7526.4}}{2\times 28}$$

Tuhia te pūtakerua o te -7526.4.

$$x=\frac{0±\frac{112\sqrt{15}i}{5}}{2\times 28}$$

Whakareatia 2 ki te 28.

$$x=\frac{0±\frac{112\sqrt{15}i}{5}}{56}$$

Nā, me whakaoti te whārite x=\frac{0±\frac{112\sqrt{15}i}{5}}{56} ina he tāpiri te ±.

$$x=\frac{2\sqrt{15}i}{5}$$

Nā, me whakaoti te whārite x=\frac{0±\frac{112\sqrt{15}i}{5}}{56} ina he tango te ±.

$$x=-\frac{2\sqrt{15}i}{5}$$

Kua oti te whārite te whakatau.

$$x=\frac{2\sqrt{15}i}{5} x=-\frac{2\sqrt{15}i}{5}$$