Whakaoti i te left(-50xright)^2-25x-500=0

$${ \left(-50x \right) }^{ 2 } -25x-500 = 0$$

Whakaoti mō x

$$x=\frac{3\sqrt{889}+1}{200}\approx 0.452241545$$

$$x=\frac{1-3\sqrt{889}}{200}\approx -0.442241545$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakarohaina te \left(-50x\right)^{2}.

$$\left(-50\right)^{2}x^{2}-25x-500=0$$

Tātaihia te -50 mā te pū o 2, kia riro ko 2500.

$$2500x^{2}-25x-500=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 2500 mō a, -25 mō b, me -500 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-25\right)±\sqrt{\left(-25\right)^{2}-4\times 2500\left(-500\right)}}{2\times 2500}$$

Pūrua -25.

$$x=\frac{-\left(-25\right)±\sqrt{625-4\times 2500\left(-500\right)}}{2\times 2500}$$

Whakareatia -4 ki te 2500.

$$x=\frac{-\left(-25\right)±\sqrt{625-10000\left(-500\right)}}{2\times 2500}$$

Whakareatia -10000 ki te -500.

$$x=\frac{-\left(-25\right)±\sqrt{625+5000000}}{2\times 2500}$$

Tāpiri 625 ki te 5000000.

$$x=\frac{-\left(-25\right)±\sqrt{5000625}}{2\times 2500}$$

Tuhia te pūtakerua o te 5000625.

$$x=\frac{-\left(-25\right)±75\sqrt{889}}{2\times 2500}$$

Ko te tauaro o -25 ko 25.

$$x=\frac{25±75\sqrt{889}}{2\times 2500}$$

Whakareatia 2 ki te 2500.

$$x=\frac{25±75\sqrt{889}}{5000}$$

Nā, me whakaoti te whārite x=\frac{25±75\sqrt{889}}{5000} ina he tāpiri te ±. Tāpiri 25 ki te 75\sqrt{889}.

$$x=\frac{75\sqrt{889}+25}{5000}$$

Whakawehe 25+75\sqrt{889} ki te 5000.

$$x=\frac{3\sqrt{889}+1}{200}$$

Nā, me whakaoti te whārite x=\frac{25±75\sqrt{889}}{5000} ina he tango te ±. Tango 75\sqrt{889} mai i 25.

$$x=\frac{25-75\sqrt{889}}{5000}$$

Whakawehe 25-75\sqrt{889} ki te 5000.

$$x=\frac{1-3\sqrt{889}}{200}$$

Kua oti te whārite te whakatau.

$$x=\frac{3\sqrt{889}+1}{200} x=\frac{1-3\sqrt{889}}{200}$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakarohaina te \left(-50x\right)^{2}.

$$\left(-50\right)^{2}x^{2}-25x-500=0$$

Tātaihia te -50 mā te pū o 2, kia riro ko 2500.

$$2500x^{2}-25x-500=0$$

Me tāpiri te 500 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$2500x^{2}-25x=500$$

Whakawehea ngā taha e rua ki te 2500.

$$\frac{2500x^{2}-25x}{2500}=\frac{500}{2500}$$

Mā te whakawehe ki te 2500 ka wetekia te whakareanga ki te 2500.

$$x^{2}+\left(-\frac{25}{2500}\right)x=\frac{500}{2500}$$

Whakahekea te hautanga \frac{-25}{2500} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 25.

$$x^{2}-\frac{1}{100}x=\frac{500}{2500}$$

Whakahekea te hautanga \frac{500}{2500} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 500.

$$x^{2}-\frac{1}{100}x=\frac{1}{5}$$

Whakawehea te -\frac{1}{100}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{1}{200}. Nā, tāpiria te pūrua o te -\frac{1}{200} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{1}{100}x+\left(-\frac{1}{200}\right)^{2}=\frac{1}{5}+\left(-\frac{1}{200}\right)^{2}$$

Pūruatia -\frac{1}{200} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{1}{100}x+\frac{1}{40000}=\frac{1}{5}+\frac{1}{40000}$$

Tāpiri \frac{1}{5} ki te \frac{1}{40000} mā te kimi i te tauraro pātahi me te tāpiri i ngā taurunga. Ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$x^{2}-\frac{1}{100}x+\frac{1}{40000}=\frac{8001}{40000}$$

Tauwehea x^{2}-\frac{1}{100}x+\frac{1}{40000}. 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}.

$$\left(x-\frac{1}{200}\right)^{2}=\frac{8001}{40000}$$

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

$$\sqrt{\left(x-\frac{1}{200}\right)^{2}}=\sqrt{\frac{8001}{40000}}$$

Whakarūnātia.

$$x-\frac{1}{200}=\frac{3\sqrt{889}}{200} x-\frac{1}{200}=-\frac{3\sqrt{889}}{200}$$

Me tāpiri \frac{1}{200} ki ngā taha e rua o te whārite.

$$x=\frac{3\sqrt{889}+1}{200} x=\frac{1-3\sqrt{889}}{200}$$