Whakaoti i te -0.007x^2+1.3x^2+0.4225=0

$$-0.007 { x }^{ 2 } +1.3 { x }^{ 2 } +0.4225=0$$

Whakaoti mō x (complex solution)

$$x=-\frac{i\times 13\sqrt{12930}}{2586}\approx -0-0.57162879i$$

$$x=\frac{i\times 13\sqrt{12930}}{2586}\approx 0.57162879i$$

Ngā Upane mā te Kimi Pūtakerua

Pahekotia te -0.007x^{2} me 1.3x^{2}, ka 1.293x^{2}.

$$1.293x^{2}+0.4225=0$$

Tangohia te 0.4225 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$1.293x^{2}=-0.4225$$

Whakawehea ngā taha e rua ki te 1.293.

$$x^{2}=\frac{-0.4225}{1.293}$$

Whakarohaina te \frac{-0.4225}{1.293} mā te whakarea i te taurunga me te tauraro ki te 10000.

$$x^{2}=\frac{-4225}{12930}$$

Whakahekea te hautanga \frac{-4225}{12930} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 5.

$$x^{2}=-\frac{845}{2586}$$

Kua oti te whārite te whakatau.

$$x=\frac{13\sqrt{12930}i}{2586} x=-\frac{13\sqrt{12930}i}{2586}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Pahekotia te -0.007x^{2} me 1.3x^{2}, ka 1.293x^{2}.

$$1.293x^{2}+0.4225=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1.293 mō a, 0 mō b, me 0.4225 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 1.293\times 0.4225}}{2\times 1.293}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 1.293\times 0.4225}}{2\times 1.293}$$

Whakareatia -4 ki te 1.293.

$$x=\frac{0±\sqrt{-5.172\times 0.4225}}{2\times 1.293}$$

Whakareatia -5.172 ki te 0.4225 mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro, ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$x=\frac{0±\sqrt{-2.18517}}{2\times 1.293}$$

Tuhia te pūtakerua o te -2.18517.

$$x=\frac{0±\frac{13\sqrt{12930}i}{1000}}{2\times 1.293}$$

Whakareatia 2 ki te 1.293.

$$x=\frac{0±\frac{13\sqrt{12930}i}{1000}}{2.586}$$

Nā, me whakaoti te whārite x=\frac{0±\frac{13\sqrt{12930}i}{1000}}{2.586} ina he tāpiri te ±.

$$x=\frac{13\sqrt{12930}i}{2586}$$

Nā, me whakaoti te whārite x=\frac{0±\frac{13\sqrt{12930}i}{1000}}{2.586} ina he tango te ±.

$$x=-\frac{13\sqrt{12930}i}{2586}$$

Kua oti te whārite te whakatau.

$$x=\frac{13\sqrt{12930}i}{2586} x=-\frac{13\sqrt{12930}i}{2586}$$