Whakaoti i te 50x^2+45+500-85=80%

$$50 { x }^{ 2 } +45+500-85=80 \%$$

Whakaoti mō x (complex solution)

$$x=-\frac{2\sqrt{1435}i}{25}\approx -0-3.030511508i$$

$$x=\frac{2\sqrt{1435}i}{25}\approx 3.030511508i$$

Ngā Upane mā te Kimi Pūtakerua

Tāpirihia te 45 ki te 500, ka 545.

$$50x^{2}+545-85=\frac{80}{100}$$

Tangohia te 85 i te 545, ka 460.

$$50x^{2}+460=\frac{80}{100}$$

Whakahekea te hautanga \frac{80}{100} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 20.

$$50x^{2}+460=\frac{4}{5}$$

Tangohia te 460 mai i ngā taha e rua.

$$50x^{2}=\frac{4}{5}-460$$

Tangohia te 460 i te \frac{4}{5}, ka -\frac{2296}{5}.

$$50x^{2}=-\frac{2296}{5}$$

Whakawehea ngā taha e rua ki te 50.

$$x^{2}=\frac{-\frac{2296}{5}}{50}$$

Tuhia te \frac{-\frac{2296}{5}}{50} hei hautanga kotahi.

$$x^{2}=\frac{-2296}{5\times 50}$$

Whakareatia te 5 ki te 50, ka 250.

$$x^{2}=\frac{-2296}{250}$$

Whakahekea te hautanga \frac{-2296}{250} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x^{2}=-\frac{1148}{125}$$

Kua oti te whārite te whakatau.

$$x=\frac{2\sqrt{1435}i}{25} x=-\frac{2\sqrt{1435}i}{25}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tāpirihia te 45 ki te 500, ka 545.

$$50x^{2}+545-85=\frac{80}{100}$$

Tangohia te 85 i te 545, ka 460.

$$50x^{2}+460=\frac{80}{100}$$

Whakahekea te hautanga \frac{80}{100} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 20.

$$50x^{2}+460=\frac{4}{5}$$

Tangohia te \frac{4}{5} mai i ngā taha e rua.

$$50x^{2}+460-\frac{4}{5}=0$$

Tangohia te \frac{4}{5} i te 460, ka \frac{2296}{5}.

$$50x^{2}+\frac{2296}{5}=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 50 mō a, 0 mō b, me \frac{2296}{5} mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 50\times \frac{2296}{5}}}{2\times 50}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 50\times \frac{2296}{5}}}{2\times 50}$$

Whakareatia -4 ki te 50.

$$x=\frac{0±\sqrt{-200\times \frac{2296}{5}}}{2\times 50}$$

Whakareatia -200 ki te \frac{2296}{5}.

$$x=\frac{0±\sqrt{-91840}}{2\times 50}$$

Tuhia te pūtakerua o te -91840.

$$x=\frac{0±8\sqrt{1435}i}{2\times 50}$$

Whakareatia 2 ki te 50.

$$x=\frac{0±8\sqrt{1435}i}{100}$$

Nā, me whakaoti te whārite x=\frac{0±8\sqrt{1435}i}{100} ina he tāpiri te ±.

$$x=\frac{2\sqrt{1435}i}{25}$$

Nā, me whakaoti te whārite x=\frac{0±8\sqrt{1435}i}{100} ina he tango te ±.

$$x=-\frac{2\sqrt{1435}i}{25}$$

Kua oti te whārite te whakatau.

$$x=\frac{2\sqrt{1435}i}{25} x=-\frac{2\sqrt{1435}i}{25}$$